Test of English as a Foreign Language

English, the third most common language spoken after Mandarin and Spanish, is spoken by around 370 to 390 million people in around 50 different countries. Many renowned universities, require their students, in the undergraduate, graduate and post graduate programs to first prove their proficiency in the English language, as an entrance criteria. This created a need for a standard test, accepted and recognized by these universities, to be created. Test of English as a Foreign Language or TOEFL as it is commonly referred to as, is such a test. This test is developed and conducted by the Educational Testing Service. TOEFL can be administered via the internet(TOEFL iBT) or can be written as a paper based test(TOEFL PBT). Written Tests are only administered in places where Internet Based Testing Centers for TOEFL are unavailable. This test score along with the applicant's other academical information becomes the foundation for their admission process. The test score scale ranges from 0 to 120, for TOEFL iBT, and from 310 to 677 for TOEFL PBT. The minimum test score acceptable, varies from university to university, depending on factors like courses undertaken or whether the applicant is an undergrad, grad or post grad.TOEFL iBTTOEFL iBT tests the four basic skills needed for effective communication namely- Reading, Speaking, Listening and Writing. They test the takers toread, listen, and then speak in response to a questionlisten and then speak in response to a questionread, listen, and then write in response to a questionThe test is 4 hours long and it is essential that all the four sections of the test be taken on the same day itself.Test FormatSECTION FORMAT TIMEREADING 3-5 passages(700words), 12-14 question each 60-100 minutesLISTENING 2–3 conversations, 5 questions each4–6 lectures, 6 questi ons each 60-90 minutes10 MINUTES BREAKSPEAKING 6 tasks which include 2 independent and 4 integrated 20 minutesWRITING 2 tasks which include 1 integrated task and1 independent task 50minutes(20 for integrated and 30 for independent)The time displayed above is not an actual representation, and may vary on the number of questions.Reading SectionThe reading sections tests the applicant's ability to, comprehend, learn and to find information from university level academic passages and texts. The questions asked in the reading section are of the following formatMultiple choice questions- asking the applicant to select a single answer from a given set of optionsMultiple choice questions asking the applicant to select an option to â€Å"insert a sentence† where it fits best in a passageQuestions with more than four choices and more than one possible correct answer.Listening SectionThis section tests the applicants ability to understand Spoken English, by testing his/her ability to un derstand lectures and conversations. The applicant is allowed to take notes while listening to the material provided. These notes will be collected at the end of the test and destroyed. Questions asked in the Listening section, are usually asked in the following formatsMultiple choice questions with a single correct answerMultiple choice questions with more than one correct answerQuestions that require the user to order eventsQuestions that require the applicant to match objects or text to categories in a chartSome questions replay a portion of the audio material provided, so that the applicant need not memorize the material before answering the question.Speaking SectionHere the applicant is tested for his ability to communicate, participate in casual conversations, respond to questions etc. This section includes six tasks that that the applicant must undertake before proceeding further. The first two task are independent speaking tasks, where the user is asked to express their opinion or idea on topics provided, or on topics that the applicant is comfortable with. The next four tasks are integrated tasks where the applicant must use more than one of their skills before responding. These skills may include reading, listening and speaking. The user is only allowed to spend 20 minutes in this section.Writing SectionThis section tests the applicants ability to present their ideas in a clear and well organized manner. Here students are required to undertake two tasks, one integrated and one independent. Independent tasks include writing essays, articles, expressing opinions etc. The student's range of grammar, vocabulary, spelling, punctuations and layout are tested under Independent tasks. Under Integrated tasks students are required to summarize, paraphrase, and cite accurate information from the source material. The total time sanctioned for both these tasks is 50 minutes. TOEFL scores are valid for 2 years. These scores are visible,10 days after the exam on the TOEFL registration website. Printed Scores are mailed after 13 days. More than 10,000 universities in around 130 countries accept TOEFL scores for their admission process. So when you plan on an education abroad, Think TOEFL.

Theo 104

Ivory Russell April 15, 2012 Theo 104 It seems as though in today’s age and time that Satan’s existence is more real and prevalent not only among society, but among Christians, as well. But, it isn’t the talk of Satan that is alarming so much as the type of attention and talk that he is receiving. Our modern day society has transformed him from being the evil, factual being that we know him as into a sinister, more humors fictional character used to make ‘great’ movies and entertainment. Producers are making a living out of Satan’s character.One of the most well known movies depicting this is Little Nicky. It depicts Satan preparing to retire from ruling Hell and trying to decide which of his three sons will take over the throne. But, when Satan decides to go ahead and keep the throne two of his children leave Hell to create their own version of Hell on earth; landing in New York City these two brother possess the political leaders of the city , freeze the gates of Hell to keep souls from going to their father, and create chaos among the mortals if New York.The movie ends with Satan’s youngest son, Nicky, saving the day, and defeating his brothers so that all of the souls, once again, can return to Satan himself. This movie is considered a comedy and opened at #2 in the North American box office. As disturbing as the film industry’s portrayal of Satan may be, it isn’t too surprising to me. What I find to be surprising, but even more so frightening, is the fact that ‘Christians’ are falling into this same trap. There are a few Christians who will speak out against such media and portrayal, but the majority will sit silently amongst themselves and simply just ‘not watch such things. But even still, there are Christians who actually believe Satan to be fictitious. In 2009, Barna done a survey indicating that 6 out of 10 Christians believe Satan to be a symbol of evil rather than a livi ng being. That is 6 out of 10 too many! But, what is the real nature of Satan? Is he really just a symbol of evil and a fictitious being? Do today’s society and film producers know something that we, as Christians, do not? The Bible says, ‘How are thou fallen from heaven, O Lucifer, son of the morning! How are thou cut down to the ground, who didst weaken the nations! Isaiah 14:12 God’s word very clearly identifies Satan as being a real being. Not a fictitious character, but rather a real, living being capable of speaking and deceiving. Satan was originally in Heaven, created as an angel. He was living with God, until pride entered into his heart and he schemed to become like God. ‘I will ascend above the heights of the clouds; I will be like the most High. ’ Isaiah 14:14 Because of the sin of pride, and because there is no room for sin in Heaven, he was kicked out along with those who followed and rebelled with him. Yet thou shalt be brought down to hell, to the sides of the pit. ’ Isaiah 14:15 Surely, if Satan were fictitious God would not have described him as a real being capable of making real decisions resulting in real consequences. Satan is not only an ‘angel gone bad,’ but a being capable of knowing, learning, deceiving, and twisting the word of God. Though evil, he is intelligent. This is supported through his ability to memorize Scripture, and twist it to what he wants it to mean.He was even able to use his knowledge of God to tempt Eve in the Garden. ‘†¦And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?†¦ God hath said, ye shall not eat of it, neither shall ye touch it. And the serpent said unto the woman, Ye shall not surely die:’ Genesis 3:1-4 Satan not only is capable of knowing what God’s word says, but is capable and will do all that he can to twist it and lead you astray. Satan is an imitator of God. His desire to be a s God is what caused him to be kicked out of Heaven.Though Satan has failed in his efforts to be like God, and though he knows he will never win against God, he still tries. You can look all around the world today and see evidence of Satan’s imitations. Men have allowed themselves to be open to such duplications that they no longer see them as Satanic or evil, but as a religion of their own. In Satan’s quest to be like God he has influenced men to the point that they have constructed their own church for him and mocked the Christian bible with their very own Satanic ‘bible. ’ Satan has even produced his own versions of prophets.But, unlike God’s prophets, these ‘prophets’ will create confusion among people, teach them false doctrines, and bring them false hopes. ‘But there were false prophets also among the people, even as there shall be false teachers among you, who privily shall bring in damnable heresies, even denying the Lord that brought them, and bring upon themselves swift destruction. And many shall follow their pernicious ways; by reason of whom the way of truth shall be evil spoken of. ’ 2 Peter 2:1-2 The Bible so unmistakably reveals Satan as a true being. Satan is real just as Christ, Himself, is real.He not only is the symbol if all things evil, but is the author of all things evil. But, if Satan is real why are Christians having so many doubts of his existence? And, if Satan is evil why are producers portraying him as something so completely different? The answers to these questions lay in the fact that Satan has done what he does best†¦deceive! ‘Be sober, be vigilant; because yours adversary the devil, as a roaring lion, walketh about, seeking whom he may devour. 1 Peter 5:8 By deceiving the nations, Satan is trying his best to defeat God.Satan thinks that by creating false doctrines and providing artificial ‘salvation’ he is keeping souls from coming to Christ. And though his deception is keeping souls from coming to Christ he is still the one who is defeated. The fact that the media is trying to portray Satan as something not to be feared, and the fact that so many Christians are being deceived, believers in Christ should be taking a stand; a stand against Satan and a stand against false doctrines. Because, ‘apart from total dependence upon God, we cannot win the victory over the devil. ’

Methods Used by Elementary Teachers in Managing Misbehavior in the Classroom Essay

Introduction In today’s society, teachers at all grade levels face a growing number of students whose behavior challenges the success of daily classroom instruction. Managing misbehavior in the classroom remains one of the persistent difficulties of teaching. Whether it is in the elementary or secondary and tertiary education, the management of the pupil’s conduct remains to be a vital part of the daily equation of effective teaching. A large part of everything students do in school is geared toward forming good habits and discipline falls right in line with this. Discipline is concerned with the development of internal behavior that enables the students to manage themselves. Every school is required by our government to maintain discipline and to issue disciplinary rules for strict compliance. They are designed to develop among students the highest standard of decency, morality and good behavior. If there’s no discipline early, there’ll likely be no discipline as an a dult, which affects job performance, family relations, among other aspects of a student’s life. The aim of discipline is to set limits restricting certain behaviors or attitudes that are seen as harmful or going against school policies, educational norms, school traditions, among others. Concrete, reasonable and fair discipline is the foundation of an effective and efficient institution. Fortunately, teachers usually are able to rely on these disciplinary rules and standard strategies for addressing classroom misbehavior, either independently or with the support of colleagues, and they are able to find a successful solution to the problem however these tactics may still fail to produce the desired outcome because of the varying degrees of differences in the attitude of teachers and students and other societal factors. While there have been gains in terms of school’s responses and significant programs and policies have already been made to lessen the occurrence of misbehaving, and improve the behavior of the students, such efforts have not been enough to cater to this rap idly growing number of cases. On the other hand, while these set of strategies are in place, enforcement remains weak. Challenges still remain in terms of translating these rules into concrete and doable actions that will address the underlying cause that bring about misbehavior in schools. It is therefore imperative to develop a stronger and comprehensive platform on treating this phenomenon that includes a wide  array of possible intervening factors, existing opportunities and limitations. Teachers must be able to work within school guidelines, connect with the students and communicate these difficulties with parents for effective teaching best takes place in a classroom with few disruptions for misbehavior. Moreover, the government, the school, the parents, and the children themselves should share responsibilities. This paper is therefore addressed to concerned professionals, agencies, and the public school administrators and teachers who are presently working hard in alignment towards eliminating the negative effects of misbehavior from public schools such as Catbalogan I Central Elementary Sch ool to other public and private institutions in the whole country. Statement of the Problem Nowadays, Filipino teachers face the spread of behavioral problems that threaten the educational system in most schools. These problems have direct influence on the learning process and the overall teaching/learning experience. Thus, more and more models of strategies are utilized by schools to combat the increasing problems. To deliberately rank the most effective means to overcome misbehavior on a more basic and intrinsic spectrum as vital and basic as public elementary schools, the study will explain and analyze the different strategies that have facilitated Catbalogan 1 Elementary School teachers in dealing with the misbehavior of Grade 5 and 6 students and how effective have they been in managing misbehavior in the classroom during the school year 2013-2014. Research Questions: 1. What are the general theories explaining the occurrence of misbehavior among children in general? * Why do students misbehave? * What are the indicators of misbehavior? * When and how could we assess if the student is already misbehaving? * Compare respondent’s approach to classroom management with Dreikurs’s approach and determine which of Dreikurs’s approaches were incorporated into the respondents’ approach. How do they incorporate them? * 2. What basic proper standards of behavior does the teacher implement in addition to the existing school behavior policies and programs in dealing with students misbehavior? 3. Which of these disciplinary methods, techniques and strategies is the most effective in the reduction and prevention of misbehavior of students in class? Thesis Statement The research intends to study the administration of discipline towards misbehavior cases in Grade 5 and 6 classes of Catbalogan 1 Central Elementary School. The study affirms that the management of existing policies and strategies used by the teachers in dealing with the problem of misbehavior still face greater challenge that it remains inadequate in the implementation because these rules and their consequences are not equally and consistently enforced. A comprehensive school behavior policy program is indispensable in meeting the needs of each school in curbing down misbehavior towards effective teaching and also in providing a positive learning experience for children. Hypotheses 1. The strategies that will be utilized greatly depend on the ability of the teachers to provide a comprehensive set of the proper standards of behavior or a behavior policy in the class. 2. Societal factors have a significant effect in properly addressing the issues of misbehavior in the classroom. 3. Teachers’ lack of awareness of the rules which requires their functions to discipline, safeguard and promote the welfare of the children has a negative effect on the behavior of the students. Student’s behavior on the other hand is directly affected by the teachers’ attitude towards them. Theoretical framework Effective teachers know that in order to truly help a student to change an inappropriate behavior, they have to get to the root causes and consider the core of the problem. When there is misbehavior, we have to stress out several external consequences of several interdependent conditions. Therefore, in order for us to identify, plan, and implement and compare the most effective strategies of intervention, it is necessary to define it in  the context of its different causes and structural features. The researcher through the examination of theories available in the literature will use the Social Discipline Model by the social psychologist, Rudolf Dreikurs. Dr. Rudolf Dreikurs, renowned educator, developed these four behavioral goals in the 1930s. He was a student and colleague of Alfred Adler, who believed that â€Å"all behavior has a purpose.† Dreikurs has written many articles and books on student behavior and much of his work can be purchased on the internet. His theories on behavior have had an enormous impact on the raising of children and classroom management models. His model is based on the four basic premises of Adler’s social theory which are: 1. Humans are social beings and their basic motivation is to belong 2. All behavior has a purpose 3. Humans are decision-making organisms 4. Humans only perceive reality and this perception may be mistaken or biased Dreikurs’ educational philosophy is â€Å"based on the philosophy of democracy, with its implied principle of human equality, and on the socio-teleological approach of the psychology of Alfred Adler. In this frame of reference, man is recognized as a social being, his actions as purposive and directed toward a goal, his personality as a unique and indivisible entity†. (Dreikurs,1968). A socio-teleological approach implies the existence of God, a higher purpose, and a natural order of things. Dreikurs believed it was possible to understand children’s misbehaviors by recognizing the four main purposes or goals of the child. The four goals of misbehavior are attention getting, the contest for power, seeking revenge, and displaying inadequacy. Dreikurs promoted the use of encouragement and logical (and natural) consequences rather than reward and punishment. Essentially, every action of the child is grounded in the idea that he is seeking his place in the group. A well-adjusted child will conform to the requirements of the group by making valuable contributions. A child who misbehaves, on the other hand, will defy the needs of the group situation in order to maintain social status. Whichever of the aforementioned goals he chooses to employ, the child believes that this is the only way he can function within the group dynamic successfully. Dreikurs states that â€Å"his goal may occasionally vary with the circumstances: he may act to attract attention at one moment, and assert his power or seek revenge at another† (Dreikurs, 1968, p.27). Regardless if the child is well-adjusted or is misbehaving, his main purpose will be social acceptance. The following are techniques that can be used to address the four goals of misbehavior Attention Getting Some students strive to be the center of attention. They do almost anything to be noticed from being argumentative to being funny. There is a lack of concern about following accepted procedure to gain recognition. Teachers and classmates find behavior by this student annoying and at times rude and unacceptable. The attention seekers may be disciplined for: disrespect, teasing, disturbing the class, being uncooperative, swearing, talking, being out of his seat, and making fun of others. Dreikurs said most students start misbehaving by seeking attention, and when this fails, they move on to more problematic goal-seeking behaviors, such as power. This is why it is important to find a thoughtful intervention in the first phase of misbehavior: attention seeking. (http://www.metu.edu.tr) Dreikurs believed that over 90% of all misbehavior is for attention. Technique towards attention Getting Behavior: 1. Minimize the Attention – Ignore the behavior, stand close by, write a note 2. Legitimize the Behavior – Create a lesson out of the behavior, have the class join in the behaviors 3. Do the Unexpected – Turn out the lights, play a musical instrument, talk to the wall 4. Distract the Student – Ask a question or a favor, change the activity 5. Recognize Appropriate Behavior – Thanks students, give a written note of congratulations 6. Move the Student – Ask the student to sit at another seat, send the student to a â€Å"thinking chair† Seeking Power and Control Wanting to be in charge or in control provides the motivation for some student misbehavior. Students with this agenda simply want their way. They don’t hesitate to take a stand on matters important to them and are often disruptive and confrontational in reaching their goal. The teacher may feel provoked, threatened or challenged by this student. The following reasons may be the basis for a referral to the office for a student who struggles for power: disobeying, disrespect, not cooperating, talking back and  disturbing the class. Often power-seeking students don’t act out until they’re assured of an audience. And from the teacher’s perspective, this is probably the worst possible time. 1. Make a Graceful Exit – Acknowledge student’s power, remove audience, table matter for later discussion, 2. Use a Time-Out 3. Apply the Consequence Seeking Revenge Lashing out or getting even is how some students compensate for real or imagined hurt feelings. The target of the revenge may be the teacher, other students, or both. Revenge may come in the form of a physical and/or psychological attack. Bullies often use revenge as their excuse for shoving or pushing, teasing, causing embarrassment and excluding others. Displaying Inadequacy Wanting to avoid repeated failure, some students appear to be discouraged and helpless. They falsely believe that they can’t live up to expectations, either their own or those of others. To compensate for this belief, they don’t attempt anything that might result in failure. They hope that others will forget about them and not hold them responsible for anything. These students may be disciplined for: not paying attention, not being prepared, being dishonest and wasting time. This phenomenon, decribed as â€Å"learned helplessness† by psychologists, is characteristic of students who fail needlessly because they do not invest their best efforts. 1. Modify Instructional Methods 2. Use Concrete Learning Materials and Computer-Enhanced Instruction 3. Teach One Step at a Time (or break instruction into smaller parts) 4. Provide Tutoring 5. Teach Positive Self-Talk and Speech 6. Teach that Mistakes are Okay 7. Build Student’s Confidence 8. Focus on Past Successes 9. Make Learning Tangible 10. Recognize Achievement No matter what the reason is for a student’s misbehavior, we are forced to respond. Some responses produce better results than others. Below is a list of both positive and negative responses by educators. Responses that usually get negative results include: 1. Reacting emotionally by being angry or making hollow threats 2. Handing out a punishment that is out of proportion to the offense 3. Reacting to misbehavior publicly 4. Reacting to a small incidence that often resolves itself 5. Making an accusation without the facts to back it up Responses that tend to get positive results include: 1. Describing the unacceptable behavior to the student 2. Pointing out how his behavior negatively impacts him and others 3. Talking with the students about what could have been a better behavior choice and why 4. Asking the student to write a goal that will help him improve his actions 5. Showing confidence in the student that his behavior goals are achievable 6. Positively reinforcing behavior that relates to student goals Dreikurs believes the best way to correct misbehavior is with logical consequences. For example, if a student doesn’t finish his homework, he stays after school to complete it. This helps the student make an association between the misbehavior and the consequences. The environmental-sociological-cultural are those theories that see the primary contributing factors to misbehavior from the immediate environment, society, or culture. Balanon also classified this model as the â€Å"environment factor† which includes physical, social, cultural and economic factors. This includes 1) environmental stress model, 2) social learning model 3) social-psychological and 4) psychosocial systems. (Rodriguez, 2006) The family systems approach by Peter Reder, Duncan Sylvia, and Gray Moira, which put significance in the relationship between family and others as relevant to the problem and analysis. It provided a framework that focuses in interpersonal, group, and institutional functioning. It is said that the concept of circularity in the systemic model emphasizes mutual influence between two or more people and the role and meaning that each person has for others must be modified and their relationship renegotiated. Family systems focus on patterns of interaction within families with particular emphasis on  communication and a psychological role adopted by family members and the view of casualty is circular involving family members. According to Rozsbaszky in Understanding the â€Å"Misbehavior† of Children Through the Theory and Research on Ego Development,(1980) , the theory of â€Å"ego development† by Jane Loevinger is a major theory of personality. According to the theory, it is a major determinant of personality characteristics in each individual whether child or adult is his or her level of ego development. Some personality characteristics are believed to be manifestations of an individual’s ego level. Personality characteristics may actually be markers or milestone traits for a particular ego level. As the child matures, he or she passes through the invariant sequence of stages of ego development, each greater cognitive and interpersonal complexity than the precedi ng stages. FIGURE 1 : Conceptual Framework of the Study Conceptual Framework Explained The figure shows a base frame which contains the respondents and the research environment which this study will be conducted. The respondents of this study are the Grade V and VI teachers of CAtbalogan I Elementary School. At the top of the base frame is a bigger frame which contains the variates as well as the process by which this study will be conducted. The study will determine the relationship shown by the double headed arrow connecting the two frames, between the Teacher’s Profile, Student’s Profile, Class Profile as to size and performance, Government Intervention, Support Groups, Family Values, Behavior of teachers towards students, behavior of students towards teachers other societal, psychological, economic, environment factors shown by the box at the right of the bigger frame, and the strategies and techniques of Grade V and VI teachers in dealing with misbehavior among students with existing school behavioral policy and legislation and programs on misbehavio r shown by the box at the left inside the bigger frame. The result of this study and the corresponding recommendations made, seen as the third frame, will serve as basis for the desired result shown in the uppermost broken lined sphere which is Positive Classromm Environment and successful and effective teaching and improved well-being of students. The desired effect depends on the independent variables which are strategies and  techniques used by Teacher-respondents, existing school behavioral policies and implementing laws regarding misbehavior. Effective implementation of these strategies and policies in schools with the cooperation and intervention of societal factors such as the family as the primary unit of society, next is the educational system, the variety of social networks, serves as important factors to attain an improved system on managing misbehavior in schools. However, this would also be measured among other intervening factors such as the profile of teachers, students and the class as to size and performance, government interventions, support groups, the values of the family of students, the behavior of teachers towards the class, the behavior of student towards teachers and other societal, psychological, economic, and environment setbacks. They include the complexity of social relationships with kin, neighbo rs, and friends, who may be sources of stress as well as support, and who may fail to reduce misbehavior even when they are trying to be emotionally supportive. Consequently above relationships of the boxes inside the bigger frame, a desired outcome is total awareness of Effective Methods towards Successful Management of Students’ Misbehavior in Catbalogan 1 thus will result to positive classroom environment and improved well being of the students. SIGNIFICANCE OF THE STUDY The study is intended to study the occurrence of misbehavior among students, its causes and the many ways to lessen its occurrence through professional responses and strategies implemented. It also represents the active struggles of teachers in dealing with the problems of behavior towards their students. The researcher hopes that this study will serve school principals to identify the behavioral problems that faced teachers in the classroom, in order to find solutions to decrease the effect of these problems on the level of teacher participation and student achievement. It also serves the educational administrations specifically the Department of Education (DepEd) to make decision to face the classroom problems through teacher training programs and useful laws. They will also know whether a certain program has already attained certain objectives. To the teachers, it will serve as a useful guide in understanding the student’s attitude and the many causes of misbehavior. Consequently, they will gain insights on which of the several  strategies is the most effective in eradicating problems of behavior among students. They could also benefit from the study through expanding their ways of improving their methods by the recommendations brought about by this study. For the students, they will increase awareness of the need to follow the standards imposed by the teachers and adapt their behaviors accordingly to the standards of proper discipline. The school administrators will also benefit from the study through acquiring ideas thus being able to lobby for policy adjustments in order to improve the current behavior policy of the school. For future researchers, this will provide a thorough and comprehensive literature for them to be able to conduct similar studies and furthermore inspire the readers to do more studies of an all encompassing discipline such as teaching and the effects of a new framework in solving misbehavior and other academic problems wh ich are much challenging and worth experimenting. Scope and Limitations This study will determine the effective strategies used by Grade 5 and 6 Teachers of Catbalogan I Central Elementary Schools in dealing with the problem of misbehavior using the descriptive – cross sectional design approach. The respondents are the Grade 5 and 6 teachers in Catbalogan I Central Elementary School, Catbalogan City. Descriptive as well as inferential statistical tools will be used in this study. This research paper is consisted of 7 parts. The first part covered the overview, objectives of the study, the methodology, frameworks applicable and review of related literature. The next part assessed the complexity of misbehavior in the classroom and the root causes root causes and effects of misbehavior. The third part examined the existing conventional strategies, theories and practices management such as â€Å"Dreikurs’s approach, which are commonly used by a majority of schools in dealing with misbehavior in comparison torespondent’s approach in the classroom. The next chapter tackled on the set of policies and programs of the Catbalogan I central Elementary School and is subsequently followed by the chapter on the best strategies the respondents perceive to be the most effective. The next part  was delved on the analysis of findings by presentation of the date gathered from the questionnaires and relevant information from Catbalogan I Central Elementary School and finally followed by the summary of findings, conclusion and recommendation. DEFINITION OF TERMS For better understanding, the following terms are hereby defined conceptually and operationally. BEHAVIOR It is the way a person behaves or acts; conducts; manners. In this study behavior mostly refer to the perception, attitude and general feeling and well being of an individual DISCIPLINE It is imparting knowledge and skill, in other words to teach. Discipline is used by teachers or parents to teach their children about expectations, guidelines and principles. Children need to be given regular discipline to be taught right from wrong and to be maintained safe SCHOOL DISCIPLINE It is the system of rules, punishments, and behavioral strategies appropriate to the regulation of children or adolescents and the maintenance of order in schools. Its aim is to control the students’ actions and behavior MISBEHAVIOR Misbehavior is a deliberate action, contrary to adult rules when a child fully understands those rules, and has the capacity to obey them mentally, emotionally, and physically. (http://www.4cforkids.org/wp-content/uploads/2009/07/misbehavior_poster.pdf) SCHOOL BEHAVIORAL POLICY It is the general principles and standards of behavior expected of pupils at the school and how that standard will be achieved, the school rules, any disciplinary penalties for breaking the rules and rewards for good behavior. BEHAVIORAL STRATEGIES Strategies can help a teacher to manage behavior in a classroom

Vision and Rewriting the Vision Statement Research Paper

Vision and Rewriting the Vision Statement - Research Paper Example An advantage of this vision statement is that it clearly defines the objectives of this institution, which are to enable students to achieve a career in the marine industry and help its students learn how to study. The second vision statement is from PennState College of Education â€Å"to be a world leader in the integration of teaching and learning, advancement of knowledge base through research and scholarship, and leadership in service and outreach† (PSCE, 2012). This vision statement is inspirational. It also clearly states the objectives of the learning institution in its goal to promote learning among its students. The third vision statement is from City College of San Francisco â€Å"providing an affordable and unparalleled learning experience in a supportive and caring environment that lead student successfully complete their goals† (CCSF, 2012). Just like the second vision statement, this one is also inspirational and clearly defines the objective of the insti tution, which is to enhance a learning environment to promote learning. A shared vision encompasses goals of various departments. Shared vision created by learning organization should be short but detailed. The partnering learning institutions face a challenge in making the vision short and detailed. The reason for this is that the shared vision statement must state future goals of each of the departments involved. The other challenge when creating shared vision comes from conflicting future goals and objectives of different departments of learning institutions. This makes it difficult to state all of them in one vision statement. The challenge of precision and content can be overcome by using the general future goals of the departments in the learning institution. Frequently, these general goals are either similar or closely related and thus, merging them into a single statement becomes easier. The vision statement I rewrite in this part is â€Å"providing an affordable and unparalleled learning

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M5C Obstacles and Pitfalls to Success - Essay Example More emphasis is put in the endeavor to attain and maintain a considerable health plan which is being inhibited by the massive heath costs and invariably rising insurance costs. Insurance costs are increasing at an alarming rate with many medical insurance pundits alleging that the high risks in the current heath status of many individuals are the contributing factor (Pauly, MacGuire & Barros, 2011). Several factors have been continuously discussed on their influence to the obstacles, pitfalls and barriers of a good health care. Significantly the status of the economy has a haphazard impact on the costs of insurance and the heath care in general. A conducive and better performing economy where virtually all levels of income to the citizens are high and the costs of living low will enhance the affordability of a successful health plan (Pauly, MacGuire & Barros, 2011). Moreover, inflation, continuously poses a big threat to the insurance and health costs. These prices are soaring high and high with the rise in inflation rates an indication of a poorly performing economy. A successful health plan needs stable and steady economic conditions which will allow the concerned parties to attain their esteemed goal (Pauly, MacGuire & Barros, 2011). As noted earlier the levels of income play a big hand in the accomplishment of a successful health plan. Evidently, this influence is demonstrated in the instance of increased propensity to save which enhances the availability of more funds to secure health services when one is rendered less productive or retires. In addition, high income illustrates a better level to afford insurance costs which with the increasing health risks, diseases and infections are continuously rising (Inhurst, 2009). Unemployment rates are another key factor influencing on the costs of health care. With high population being unemployment and rising dependency levels many insurance providers are finding it inevitable to raise their costs

US-Britain industrial power Essay Example | Topics and Well Written Essays - 1750 words

US-Britain industrial power - Essay Example The Britain remained evidently predominant in the nineteenth century among the world powers as consequence of tremendous economic and industrial expansion in the eighteenth century. The British firms had expanded and export trade boomed vigorously in the industrial revolution.This paper investigates into the reasons that enabled the United States to replace the Britain as the world's leading industrial power after the time when Britain used to dominate the world with its industrial strength. Evidently, there happened to be several causes underlying the sharp decline in the British dominance among all the powerful countries in the world. In the same manner, there were various reasons that served to be the supporting elements for the economy and industry of United States to supersede the position of Britain.Apparently there happened to be abounding reasons behind the deterioration of British industrial and economic power in the late nineteenth century. Britain's economic diminution was in fact a consequence of the decline in the country's industrial potency that happened to be the backbone of the country's growth in the eighteenth century. However, this industrial failure did not erupt out of nothing, rather it too was an aftermath of several factors and events responsible for undermining the British industrial ascendance in the world.One of the pre-eminent causes of the failure of British industrial power was also the country's technical training and education system. The country, due to its highly advanced technical training system, produced and accumulated a large number of trained and high calibre workers for some industries. This turned out to be negative for various industrial sectors in the long run, as the country immensely began to lose unskilled workers that could perform duties on machines in the factory. This problem was faced by most of the industries in Britain, causing them to run high on costs and consequently low on profits. The British industry also lacked the most substantial ingredient i.e., machine tools required for technological excogitation in the manufacturing sector of the industry. Britain remained far behind on this ground that could have otherwise backed the deteriorating industrial strength of the country. The machine tool industry had been flourishing in the early period of British industrial development but the growth in this industry came to a gradual halt in the early twentieth century. This backwardness marked the inability of British industry to cope with the technological prerequisites of that era and the country seriously lacked behind on the technological edge. Another significant factors underlying the fall of British dominance was also that it seriously lagged on the ground of export in the late nineteenth century as compared to United States. The growth in export witnessed in the earlier decades started to tumble down and imports, on the contrary, took on a rising trend. At this time, most prominently, the United States was advancing in export trade through technological advancement and thus started to captivate even the portions of markets in Britain. This had a severe impact on the British economy and thus it started to lose dominance over other countries. This happened primarily because the Britain failed to advance in terms of new technology and as a result, the country's export trade started to decline. Free trade policies inflicted serious harms to the British industrial expansion. The country perpetually adopted the free trade policy enhancing the free flow of imported goods into the market without any restriction. This resulted in an outbreak of international

The Battles of Gettysburg and Vicksburg Essay Example | Topics and Well Written Essays - 1500 words

The Battles of Gettysburg and Vicksburg - Essay Example In fact, some scholars would estimate that without the Civil War the United States might never have become the country that it became. More so, if it were not for two definitive battles of the Civil War, the Battles of Vicksburg and Gettysburg, then the United States we built would be very different from the one we have today; if we survived at all as a nation. That said understanding the importance of these battles will help us to comprehend why these battles are so significant and if they were such definitive â€Å"turning points† in the war, then why did the war continue on, nearly, another 2 years? By finding the answers to these questions will grant us a greater, broader, picture of how the United States became the country we are today. History . The definitive battles of Vicksburg and Gettysburg did not occur until 1863, the Civil War began 2 years earlier. The causes of the Civil War can be summarized in 5 specific contributory elements. In fact, these tensions had been growing since the founding of this country in 1776. 1. The Economic & Social Differences between North and South. By the late 1700s cotton crops were incredibly valuable and profitable. The South developed an agricultural, one crop economy. They were exclusively dependent on the success and sail of their cotton crops and on the inexpensive slave labor that tended them. The North was focused on city life and industrialization. They could already compete with the South’s ability to clean, process, and manufacturer cotton goods. 2. State vs. Federal Rights. Many in America pushed for the supremacy of state’s individual rights and that they should have the right to determine what federal involvement they would accept. While others pushed for greater federal government to unify and force the hand of states. 3. Slave and Non-Slave State Proponents. The argument over whether new states formed would be slave states, free states, or would have the right to choose for themselve s was a heated one. This created serious division between supporters and opposers of slavery in the United States. 4. Growth of the Abolition Movement. The Abolitionist movement, further inspired by the publishing of â€Å"Uncle Tom’s Cabin† and the passing of the Fugitive Slave Act, fueled Northern disdain and hatred for Southern slave-owners. 5. The Election of Abraham Lincoln. Although tensions were already high, Lincoln’s election inspired South Carolina to submit its intention to secede from the United States because Lincoln favored northern interests, and was opposed to slavery. Even before Lincoln took the office, Florida, Mississippi, Texas, Louisiana, and Georgia, also, intended to join South Carolina (Kelly 2013). By 1861 Fort Sumter, in South Carolina’s Charleston Harbor, contained the last federal holding within the Southern seceding states. Cut off from supplies and reinforcements, the men of Fort Sumter were suffering. On April 11, 1863 Conf ederate soldiers led by Jefferson C, Davis, no relation to the Confederate President, ordered the evacuation of Fort Sumter, delivered personally to Union Major Robert Anderson. Although Anderson thanked the envoy for the courteous and respectfully presented request, he declined to obey the order. As the Confederate envoy left the Fort, it would be only a few short hours before, at 4:30 in the morning; the first battle of Civil War would be fought. Confederate General Pierre Gustavo Beauregard ordered his men to open fire

Globalization and Strategic Planning Essay Example | Topics and Well Written Essays - 250 words

Globalization and Strategic Planning - Essay Example In this case, in order to facilitate collaboration in the organization, Americare has been recruiting numerous interns, to offer them a chance of making crucial contribution through their membership in Global Partnership team (Americares, 2013). Cooperation refers to process of working together in a way that contributes to achievement of a common objective (Forest, 2003). All interns in Americare are offered a chance to be involved in all development programs via a target of donor and prospectus. Moreover, this organization offers them other roles such as providing support via general administrative supporting and attending events, maintenance of donor files and helping in preparation of visits and regional trips (Americares, 2013). In this case, the organization operates through the cooperation of the interns; thus, they are able to execute their mandate. According to Forest (2003), coordination is organizing and ensuring that different parts or things are operating simultaneously in order to achieve a certain objective with minimum problems. In this case, AmeriCares makes a substantial contribution in facilitating communication among the interns, through their administrative support (Americares, 2013). In this case, communication among team members is well coordinated through ways of contacting them through newsletters and other printed materials. Furthermore, vendors are coordinated to facilitate timely delivery of materials that are needed for the organization to operate effectively. Forest, C. (2003). Empowerment skills for family workers: A worker handbook. Cornell University. Retrieved on Jan 7 2012 from

Equality of Women and Men According to Locke Essay

Equality of Women and Men According to Locke - Essay Example As a political philosopher as well as a social psychologist, John Locke remained an outspoken and vehement supporter of equal rights in a society that is governed. He attributed these rights to include right to life, liberty as well as property. Locke’s belief on the legitimacy of government argued that such powers of the government rested on the citizens and it ought to result from the basis of equality. His support for equality is evidenced through his support of religious beliefs and religion where his philosophical basis of his idea is based on the availability of equality in the state of nature. Once man leave the state of nature to form governments, the role of state of nature remains with men. As such, Locke argues that in mankind races as well as families throughout the whole world, every person is equal to each other with neither one individual allowed to be on top of the other. As such Locke describes the equality in the state of nature as based on the concept of rec iprocal with every person having equal power to the other. According to Locke, all creatures of the same species possess equal advantages of nature and as such, none of the creatures from the same species ought to posses more rights than the other. Therefore, assured equality serves as the basis behind man’s agreement to enter a society. Throughout this discussion, it is apparent that Locke creates tension to the audience through avoiding the topic of women in politics. . Locke keeps on referring to men in the formation of the state of nature.

Meeting the Customer Needs Essay Example | Topics and Well Written Essays - 5000 words

Meeting the Customer Needs - Essay Example From this study it is clear that the most important question is how to know the specific needs of the customers related to some specific products. The marketing research plays the vital role in this case. The survey design and the questionnaire design play the major role to identify the customer needs. Through the proper data collection and analyzing the data are the most appropriate way to find out the customer needs and to satisfy the needs accordingly. In this particular case the target organization is the McDonald’s.This paper highlights that  maintaining a great service quality and the product quality are all about understanding the requirements of the customers and delivering the tailor-made services to satisfy them.   Understanding the customer behavior is another very important factor to be focused on to run a successful business. However, these are the basic rules to delivering satisfying services. The measurement of the steps taken towards the customer satisfacti on is also very important. The primary and secondary data are important to support the outcome of the services related to the customer satisfaction. In regards to this research, the secondary data used are gathered from the Internet, journals and other publications in order to get basic information about the nature of the influences of the customer satisfaction. And the primary data are collected from the survey made from the sample size of 50 people selected randomly.... It is very vital to understand the importance of the customer satisfactions. Customer needs are the base of any business. However, the most important question is how to know the specific needs of the customers related to some specific products. The marketing research plays the vital role in this case. The survey design and the questionnaire design play the major role to identify the customer needs. Through the proper data collection and analyzing the data are the most appropriate way to find out the customer needs and to satisfy the needs accordingly. In this particular case the target organization is the McDonald’s. Introduction: Maintaining a great service quality and the product quality are all about understanding the requirements of the customers and delivering the tailor-made services to satisfy them. Understanding the customer behavior is another very important factor to be focused on to run a successful business. However, these are the basic rules to delivering satisfyi ng services. The measurement of the steps taken towards the customer satisfaction is also very important. The primary and secondary data are important to support the outcome of the services related to the customer satisfaction. In regards to this research, the secondary data used are gathered from the Internet, journals and other publications in order to get basic information about the nature of the influences of the customer satisfaction. And the primary data are collected from the survey made from the sample size of 50 people selected randomly. McDonald’s has been taken as the target brand in this case. The whole paper is stratified into five chapters and each chapter has its own relevance to prove the importance of the customer satisfaction to win

Twenty20 and World Cup Essay Example for Free

Twenty20 and World Cup Essay Essay on furious version of t20 cricket match in India | Essay www.publishyourarticles.net//essay/essay-on-furious-version-of-t20-cri? Cricket is game internationally recognized as an instrument for the establishment of world peace. Teams from far and remote corners of the world  visit the Cricket Twenty20: Latest News on Cricket Twenty20 Outlook www.outlookindia.com/taghome.aspx?tag=101881%20Twenty20? See Cricket Twenty20 Latest News, Latest updates Photos of Cricket Twenty20 on Outlook India. T20 World Cup: India tripped, fell, never got up. Why? Is the IPL hurting the chances of fit players defending India in the www.civilserviceindia.com †º Subject?

The Cinderella Myth Essay Example for Free

The Cinderella Myth Essay The tale of Cinderella is encoded as a text of patriarchal moral instruction in which a sense of female agency will always by definition be absent. In this folk tale, which is also a fairytale, female character is positioned in terms of what it is not: not dominant, not powerful, not male. Cinderella herself, non-hero of a dubious tale, evinces more depth than most archetypes. She is capable of developing relationships, meting forgiveness, manipulating her own destiny, even of attracting magical help. This latter suggests a divine personage, with whom ancient myth is rife, but in fact there is never any indication that Cinderella is inhuman. On the contrary, her essential humanity is her salvation. These qualities on their own make Cinderella an anomaly among fairytale principals: she is given no journey, no quest, no troll to enrage or woo, but permitted to stay at home (albeit in a life of unrelieved drudgery). Although one of three sisters, she does not best them in riddles or games of strength or chance; even the sewing for which she is punished is not her own. Cinderella does not return from the party with a prize but (as I will show, I will shout) the opposite: she comes home missing what she had when she set out. Cinderella does not experience any perceivable growth or transformation with the exception of the tangible one directed by her magic guide—one which is also undone. We can read Cinderella as a mythical character only because of what she means to us as women. But that is enough. By virtue of what Cinderella represents to contemporary women, the character of Cinderella passed from her fairytale origins to mythical proportions. Cinderella has escaped the bounds of her own story. Cinderella defines girls first choice for a romantic partner, the strictures of friendship and obedience that girls are trained to uphold, unconditional family love and, not least, ideals of personal appearance and deportment. Cinderella demonstrates the potential of even the least socially advantaged female to achieve public success, the ability of the meek to triumph over the (female) competition, the trick of appearing to be what one is not. These are important techniques in the battle for male approval. If we have impressed Cinderella into service as a myth, it is because we need to look up and forward to a figure who has successfully navigated the obstacles on the distinctly female journey. Cinderellas rags-to-riches story inspires females to prevail against improbable odds. We do not believe  in myths because of some inherent truth in them, but because they substantiate what we most wish to be true: Cinderella is a falsehood painted as possibility. What we worship in her is not what she is but what she gets; by subscribing to the myth of Cinderella, we sustain our collective female belief in wealth, beauty, and revenge. New Origins Folktales had their origins in oral accounts, stories told by people before the advent of writing, or before someone determined them worthy of literary transcription. Grimm Brothers Jacob and Wilhelm did not, in an original creative act, write the tales published under their names, but went out as folklorists (before there was such a profession) into the countryside, like anthropologists in their wilds, and listened. What they brought back they then edited, like the good ethical binary German men they were: anything that didnt suit their Christian standards simply disappeared. I have read transcriptions and abstracts of their notes and wondered at the absence of certain types of tales. Stories about children surviving on their own, or women leaving the husbands who beat them, somehow never made it to press; concurrently, stories about Jews being robbed and hung in thorn trees, or torn apart by dogs while (mendacious) villagers laughed, stayed in. The Grimms were very careful not to let what they heard get in the way of what they wrote. Charles Perrault held the same view, concerned lest women and other children go astray. Both Perrault and the Brothers Grimm published these folktales as if they were their own—under their own professionally upstanding names, and not as anthropological records but as literary fictions. The performance of meaning for fairy tales becomes both an intratextual and an extratextual matter, one enacted by (re)writers of the tale, who rescript stories passed on to them, and by its readers, who collaborate with the (re)writers to negotiate yet another production of textual meaning (Tatar 277). Although old wives may have originally imparted the stories we read today, the power and authority of writing sat fast in the hands of male scholars; publication, moreover, was granted to the wealthy. For each fairy tale, Kindermà ¤rche, folk legend and myth with which we are now familiar, there are possibly thousands for which there is no record. Folk legend, like history, is selective. Cinderella was similarly written (or transcribed) from oral accounts as a piece of moral instruction.  A Cinderella by any other name exists in a variety of languages and cultures,1 with many culturally-revealing alterations to the basic storyline, most telling us of a poor but beautiful girl who, by going to a party on the hill, wins the attention of a wealthy man. Look what the right pair of shoes will do for you. Cinderellas story is a curious one. Many of us know this tale in its modern extensions but cannot say how we know it—whether we read it in a childs picture-book, watched Disneys animated version, saw a movie with human actors unanimated by comparison, or fell in love with the ash-girl in her other forms (including in Dickens revival). Indeed, Cinderella is legion: as Barbie in diversely perfect incarnations, the heroine of almost any romance novel, new and sometimes relevant literary concepts (for instance, the Cinderella complex, the whore with a heart of gold). 2 Bernard Shaws drama Pygmalion presents another instance of male bonding conducted through the service of a woman, in this case one who believes that she can only win by trying, as she has started with nothing. To his credit, Shaw allows the character to shove off at the end, bearing her body away, but to have true love and devotion this Cinderella must give up all pretenses to education. Education therefore becomes a pretense. Further transformed as the Lerner and Lowe musical My Fair Lady,3 the music ends with a new-made woman who newly makes man: Eliza converts her creators. The underlying message is one Mary Shelley crafted a hundred years earlier: Frankenstein has no loyalty. But in this case the monster manages to marry one of the scientists. Both Pygmalion stories are commercial perversions of an ancient Greek myth that performed a service for its culture. In the original, a male artist falls in love with his own sculpture, surely an intriguing commentary on the power of art to seduce even its own creator, and a warning to gaze on verisimilitude with suspicion. This brings us to Hollywoods contemporary Pretty Woman and another Disneyized threat, The Little Mermaid (if there is a hell, then Hans Christian Anderson is now in it). In these movies Cinderella transforms from foul and fish into a lady that only proves how far women will go to change for their men. As Oedipus provides a model for the male (kill Daddy, bed Mommy), so Cinderella serves the female, directing us to similarly anti-social behaviors and antipathetic familial relations: to hate and compete with other females, suffer in silence, and seek rapport with males  through the mysteries of flirtation, fashion and marital fitness. Fortunately for women, this involves only virtuous activities, easily enough acquired in the observance of girlhood duties: cleaning, cooking, sewing, nurturing and displaying ourselves publicly, all the while taking up little space. Taken to its logical conclusion, woman herself at last disappears from view. This is true in the story of Cinderella, as we shall see. Absence Let it be known that the ballerina is not a woman dancing; that, within those juxtaposed motifs, she is not a woman, but a metaphor that summarizes one of the elemental aspects of our form, sword, goblet, etc., and that she is not dancing, suggesting, by the wonder of ellipses or bounds, with a corporeal writing, that which would take entire paragraphs of dialogued as well as descriptive prose to express in written composition: a poem detached from all instruments of the scribe (Mallarmà ©, Oeuvres Completes4). One of the first absences in the text occurs in translation of Cinderella from an earlier publication in French5 to English—the absence of a word. It is a simple word and a little loss that heralds an enormous and important one: exchange of the French velours (velvet) for verre (glass). In the centrality of the image conjured by its sign, this Word reads as Logos for the remaining popularized text. It is an understandable mistake given the hardships of transcribing in the field (from which Charles Perrault, at least, copied out his manuscripts), of hearing and absorbing frank orality and then transforming it to arid print. The terminological difference, however, leaves women literally walking on glass, each step a faux pas. How does one navigate on such a fragile basis? This may be interesting to women who wonder how Cinderella got through the night in those shoes. Cinderellas new shoes are truly, clearly, invisible, her feet naked to all eyes. But worse —she must dance in an unforgiving shoe (dancing for the first time in public, mind you)—which at any moment threatens to break, replace her barefoot, bloody, and utterly helpless. How carefully she must step. A good thing the Prince has learned to dance. To comprehend the magnitude of this error—estrangement of the word and actions of our young charwoman—we are forced to retrace the steps of that perilous slipper, magicked into being with the rest of Cinderellas fancy outfit. There is no honest explanation for why the slipper remains as testimony—why, if the shoe fits, it drops. Moments earlier, we are told, the young woman was gaily dancing in this very shoe; surely it would have fallen off then, in the endless (and, as dancers know) breathlessly swift rounds of the older Austrian waltz. But after a night of aerobics indoors, the woman rushes outside and immediately loses a shoe. This mistranslation points us towards understanding the slipper as a prominent signifier, rather than towards seeing some more substantial object: glass operates as a red flag, leading us to a fanciful but ultimately unnecessary correction of an image. Glass breaks, it is true (although in the story it does not, at least overtly). But in the French source material the shoes were velvet. Velvet, a word strongly associated with skin (more so than glass), tears. It is strong, soft, stretchy and pliable. A velvet slipper can be left on the road and retrieved and can still be worn in a ragged condition. Not so glass. So while glass attracts our attention, velvet rubs us better. Something velvet has been lost. And found. If the slippers loss signifies another loss, the slipper signifies another slip. It is troubling that only one item retains its shape (the shape of magic) after the ball, when everything else has returned to its poor normalcy, right down to the golden pumpkin. If everything is magical, then the slippers exclusion makes no logical sense in the story. But without the slipper as a calling card, a sort of invitation to be stepped on, the Prince may never find Cinderella in the sea of women vying for his notice. Conversely, it is not clear to me now why the Prince has to find her. The story dazzles us with finery, which we all too readily see as refinement. In the spell of the lost slipper, we overlook the more obvious intrusion of the Prince himself, and in the absence of honest cogitation conclude that he must be the one for Cinderella. (Its true he is the only one, but in modern times that is not as good a reason as it once was.) Having had no time to know Cinderella as a woman apart from her unpleasant family, we have certainly failed to meet the Prince, and know nothing of this man except that he is extraordinarily superficial, a late bloomer, and wholly dependent upon his parents. In the remainder of the tale he develops as a foot fetishist. At no point in the story are we logically convinced that these two should be together, that the Prince is worthy of our supposed heroine, or heroic himself. Cinderella is not particularly romantic, even after the finding of the slipper that initiates a sordid (wo)manhunt. The  objective of this search is a stranger who clearly wants to hide; otherwise she would have answered the call. (Her sequestration at home in a locked house is far from likely, given that a principal domestic duty is emptying the char outside, and her name signifies her as that domestic.) And despite his hunting, there is no reason to think that a prince is going to be excited to end up with a poor ragged girl with ashes on her hands—never mind the in-laws. On the face of it, what Cinderella lost at the ball is a shoe, but we do her an injustice if we look only at her instructions (particularly as she has already ignored those of her stepmother) and neglect her feelings at the moment of flight. Cinderella is now in a palace, a place of possible refuge, safe from her family. The Prince likes her. But at the striking of the clock—no, the calling of the watchman or ringing of the bells—she gets scared and runs away. Modern detectives would phrase this differently: Cinderella exits the party late, leaving behind material evidence of her existence. (Without this the Prince might have thought that Cinderella was a fantasy.) She runs as fast as she can in an effort to beat time and find a way home. (If shed had a mother she would have known better than to go to a party where she doesnt know anyone: anything can happen at a party.) Then Cinderella loses her velvet, and the Prince gets it. (You decide what went on at that party.) And there is another ending, suggested by what is not stated in the story: Cinderella disappears from the party, last seen in the company of a prince. Passers-by report having seen a poor woman in tattered clothes, sitting in the middle of the carriage-track massaging her feet. This is the last either woman was seen. Police are now searching for this beggar whom, they believe, may have murdered a foreign princess as she left the party, probably for money. Anyone knowing the whereabouts of (but what is her name?) an anonymous princess, please contact this writer. Presentation of any story results in commission of at least two versions—the story that is told and the one we hear. I propose a tertiary rendition, that of the story we do not hear because it is not told—not, that is, forcefully sounded. Were we to listen to the spaces, as artists from Aaron Copland to Noah Ben Shea have reminded us, we would hear those speaking parts. The heard Cinderella is, despite its magic and fantasy, the authoritative edition; the unheard Cinderella is the practical, plodding story that might bring us to furious tears rather than ecstasy. A moment ago I suggested how  Cinderella might seem to an outsider, one not as privy to events as she. Underlying that suggestion is another one, that the writer or teller of the well-known Cinderella is either Cinderella herself or a close companion, as indicated by the naï ¿ ½ve credulity of the story itself. But that quality we have come to accept in the folktale genre, one which causes us to reflect upon the medieval notion of story-telling and which tells us much about religious tradition of belief in that period. Now I wish to produce something different: a case history of poor Cinderella, the pieces and bits of her life which may have been discarded by her original creator/story-tellers. Again this is an unheard story, but now it is also unspeakable. I speak as a caseworker in the Womens Shelter: Cinderella gave Intake the following story: Her mother died when Cinderella was perhaps five. Her father remarried a year later. Two older stepsisters were at the wedding, aged between eight and twelve; the stepmothers first husband died when a nearby witchs cottage burned down suspicion of arson. Almost immediately, and for the next twelve years, Cinderella was beaten regularly by her stepmother; she showed us an early scar, located on the upper left thigh, from a fire poker. Cinderellas father fell ill probably Plague and died date uncertain. The sisters began to kick, taunt, pull her hair and feed her bugs. When Cin began her menses, she was locked in a closet for? some extended time. There seems to have been a change in the familys finances at this point; the last remaining servant was let go, or left, and Cin took over all chores. She was probably eleven years old when she was first sexually assaulted, by the eldest stepsister. The abuse was repeated periodically until this day. Cin believes that her stepmother does not know of this, but C- does not dare tell her. C- sneaked off to watch the Grand Ball and, once in the estate and aided by strong drink says she had a bout with a stableboy she made it upstairs disguised as a maid, entered a room and borrowed a gown. She then appeared in the ballroom. The Prince danced with her, drew her into a private room, and seduced her not rape? C- wont say the word then returned to the party. C- fled wearing only underclothing and carrying her shoes in her hands. Outside she dropped a shoe without noticing until she got home; the other shoe is in her garret. We have all received, of course, the Royal  Proclamation, and know that Prince Ode is hunting for the owner of something in his possession. Cinderella came to the Shelter because she believes that he means to find her, take her away, and kill her. The case above, common enough in the lives of women, is not what we know as Cinderella but, given the circumstances of the folktale, its bizarre elements and strange silences, it could have been. In re-telling it I invite the reader to think how reading that as a child might have influenced her life, her love for housework, her attitudes towards men, and her desire to marry early. My Cinderella Confession A current trend in scholarship, at least printed scholarship, is self-reflexivity. The speaker is expected to identify herself, admitting her biases (as if the reader could not detect them) so as not to hide behind the formality of academic writing. In this vein I step forward and make confession, presenting some personal limitations regarding the story of Cinderella. Despite all I know about Cinderella, regardless of all that currently annoys me in the story, I confess that as a child I did identify with Cinderella. I liked animals. I liked pumpkin. I lived in a small room. When I went to parties I had a curfew —and it was unreasonable. I couldnt sew, and needed help in home economics. I went barefoot most of the time. It seems I never got dessert, possibly because I often lost things on the way home. I had to do such hard chores that I investigated child labor laws. I had two older sisters and, although they are regular sisters rather than stepsisters, they often seemed very wicked indeed. So what if they werent ugly, my feet were much smaller than theirs. (Then.) Because of them I wore hand-me-downs. (Then.) You see how it all fits. So although I was not a beautiful golden-haired orphan (my natural color is sun-bleached brunette), kept in a dungeon or an attic (I adored my aunts basement), forced to clean ashes from the hearth (we had a wall furnace) and befriended only by mice (we had large dogs), I did think that eventually someone would come and take me away from all this. I even learned to waltz. But I didnt meet any princes. The Conventions of Class Cinderella begins with Cinderellas primary absence: her mother. In fairytales, motherlessness indicates an absence of quality attention and the  necessity (given the staggering amount of handiwork done at home) for men to remarry. Their second wives are invariably brutish, and fathers die off like flies. Female children raised by these monstrous women are lucky to be married, while still children, to ugly old men —thus escaping beatings, beheadings, being poisoned, cooked, frozen, sold, or accidentally left somewhere awful. Male children with stepmothers tend to seek their fortunes at an early age, so as to find their own women to punish. The next absence in Cinderellas life is a father. Is it only that absent parents are common to the childhood fairytales which govern our memories and learning patterns, thus wending their way into our literary texts, or does this trope stand for more a founding absence, like the founding murder Oedipus is said to represent? The next absences we hear about in Cinderella are, in order: clothes, shelter, appropriate work, friends, and opportunities to socialize (with humans). It is at this point in the story that Cinderella encounters magic, something generally absent beyond fairytales. Or does she merely recognize the magic in her life? For it seems as if the Fairy Godmother were always there, available, like Glinda the Good Witch, to drop in when you needed direction. From that point on it is apparent what else Cinderella lacks: transportation, a formal dress and decent shoes. The final absence is Time. Even her Fairy Godmother gives her very little— as we find out later, just enough. After Cinderella loses the shoe in escaping (too late) from the party, she is plunged back into the animal world she dominates, shorn of finery, reduced to essentials. She returns to the level of minimal survival. Thank goodness the Prince is already searching, his spies canvassing for little feet. Cinderella will soon be lifted up, placed on a horse or in a carriage, and transported to a world of wealth and satisfaction with a big house and a good family. (I hope I didnt ruin the story for you.) On a basic moral level the instructions are clear as glass: good triumphs over bad, beauty over its repulsive opposite. Cinderella is intimately associated with nature, as we are told several times: through the animals which, like she, become domesticated; through her beauty which, in the tradition of the Aesthetic experience, demonstrates its superiority over homeliness. (Homeliness? What is homely, really, but housewifely, comfortable, and familiar —and therefore contemptible?) From our perspective of identification with Cinderella (wed hardly choose to identify with ugly,  nasty women) these females, older than she and more mature, are females prepared to party, women rather than girls, and not real (biologically real) sisters. Partly because of the brevity of the story and paucity of detail, this suggests that they, mere step-sisters, are somehow unnatural. Beyond the natural beauty that testifies to Cinderellas (yet unrealized) status, her elevation over this unconnected family is physically represented by spatial signifiers: imprisonment in an attic, conveyance in a horse-drawn coach, and finally marriage into a royal family. Above all, Cinderellas most natural gift is magic: the girls beauty and (its) charm shine brightly through mere rags. This is so apparent that it is noticed immediately by a prince—a man born into an entirely different milieu, to wealthy and indulgent parents. The story asks us, among other things, to anticipate that such a wedding of opposites will work. In fact, fairy tale happenstance and happily-ever-afters aside it just might, and because of Cinderellas nature. The Prince, culturally her Other, is the aesthetic brother of Cinderella. The kinkiness is just beginning. We customarily avoid class in reading and rewriting folklore, but Cinderella affords a remarkable discussion. Before the Prince lays eyes on her, Cinderella does not exist in the legal and economic awareness of her country. She pops into being at a party, relatively mature, decorated, and provocatively displayed. It is not a party for poor people; poverty is absent from the ball. But that in itself is an absurd notion: naturally the castle is full of servants, and most are penniless; one can only say that no poor people are present because poor people are beneath the notice of the wealthy population, invisible. This fact has not changed. Cinderella gets the invitation because it goes to the house in which she lives, a place where she is kept captive by her poverty. She seems not to have been born into the lower class (otherwise she would never have been able to get through the castle gates, let alone waltz), but fell into deprivation through the death of her parents. Who can really blame the stepmother for not wanting to take care of a girl with whom she had no real relation? Biology speaks: woman must protect her own offspring—particularly if the physical attractiveness of another female threatens their own reproductive success. The absence of Cinderellas own mother is unremarkable, superficial, unless one regards it as a fundamental absence, the one upon which the half-orphans  rags-to-riches story is initially built: through the fathers emotional absence, Cinderellas mother is replaced by a non blood-relation whose own issues of reproductive success create class strife and difference within the family; the girl is faced with rival kin; and finally a mystical figure intrudes from the other world, faintly identifiable as her mother (the magic helper styles herself a Fairy Godmother) but granting no more than material assistance. Transformation of animals into human servants,6 and their disappearance at midnight, symbolically expresses the absence of the lower classes, which serve the upper class as if animals. When we observe how Walt Disney attempted to fill in the absences in the text with additional animal habitation, this concept becomes clearer. Disney explains Cinderellas primary absence by the increased presence of animals that evidently take the place of a mother. With the appearance of the stepmother and two daughters the animals are replaced, and abandoned as Cinderella had been. An absence of family acknowledgement is discernible in Cinderella herself who, regaining the humble form of a scullery maid, becomes unrecognizable—virtually invisible—to her own family. The means by which Cinderella will eventually succeed is over-determined by class: she must physically impress her Prince and lord at court, and later fit his image of the perfect (small) woman at home. Still she requires a bit of magic. The story presents an array of questionable absences, none of them textually answered. Why is there a ball? Only because of the Princes failure to get a date on his own. His folks have to arrange something, to find women for him. Cinderella attends a party meant not for her but the beautiful people associated with money and fame. We privately know that Cinderella really belongs to this group; therefore we suspend our disbelief at the unlikelihood of her ever getting there. At the moment of Cinderellas entry, a representative of the poor actually becomes visible to rich people. But she is not really poor, is she? The tale does not end with Cinderella speaking in the public square, peasants invited up to the castle for lunch—in short with the French Revolution. (If it did, Cinderellas own head would roll.) She ascends, making aliyah; the rest of the lower-class remains in galut (the Diaspora). In fact, in the hands of Disney, Cinderella turns into a girl (few of Disneys female heroines are women)7 who sings as she is dressed—oh, those happy peasants!—in accordance with the tradition of  musical theatre to sing instead of enjoying a useful discussion. Everything stops while we listen to the same few lines being repeated. The formula recurs in nearly every Disney movie: when animals, peasants and racial minorities show up its time for a song.8 Do children want a story interrupted with a song? As a child I hated that sort of thing. Surely we must question for whom these stories, and their cinematic adaptations, are truly meant, written, animated, shown and sold. Jacqueline Rose points to the impossibility of childrens literature as a genre ostensibly for children, but written by adults, while in the marketplace it is adults who (because of their economic position) are the true consumers. It is even the adult who reads the book (aloud) to the children. Thus it is an adults version of the childs world which is manufactured through the aegis of childrens literature. Childrens fiction, says Rose, sets up a world in which the adult comes first (author, maker, giver) and the child comes after (reader, product, receiver) (Rose 1-2). So what is it that adults want children to understand from the story of Cinderella? Female Relationships One of the horrors of Cinderellas tale is the moment when she flees the castle and its famous ball. She is running, running, running away from the bright lights, the fun, the food, the nice guy, running to keep a date imposed by the Good Witch. This is a moment of horror not because she has to leave the party: shes pretty young, high time she went home. (Anyway she wouldnt want the Prince to think she was easy.) No, it is horrible because of the Fear of Public Exposure. If there is one thing that would compel me to leave a good party it would be the fear that my clothing would disappear. She runs out the door, the gate, goes down those steps, shes just off the grounds, and poof! there it goes. Fortunately she is not standing there naked, but we couldnt be sure of that beforehand. For a child to imagine being naked in public is terrible; so what if only the animals can see? There is no good explanation why the Fairy Godmother add this potential punishment to the assistance she gives Cinderella, there is no point. In my mind, something is missing from the story, something vitally important. Why is she set up in this way? What we do see in Cinderella is a tale of perfidy and female treachery. The bad characters are all female. How can one speak of a female absence in Cinderella, when it would seem that almost all of the  characters are female? But these people consist of a good but romantically stupid girl who prefers to accept the ill treatment of her step-family rather than to pack up the mice and leave; two step-sisters, ugly mean and very ugly, who are indistinguishable from the other, except through Disneys putrid use of color; an evil step-mother, also ugly; a strange woman who shows up once in a lifetime, twice if you subscribe to the Disney account. (Where was she the previous sixteen years? Thanks a lot, Mother.) Female hatred. Female sabotage. Female jealousy. These are all shown us repeatedly in Cinderella as is. We discover that the way to win a prince is over the ugly bodies of our competitors, who are similarly trying to cut our throats. Beauty on its own is not enough: you have to be seen by the right people. You must triumph over those who would hide your beauty. You must outdo them. No wonder female friendships are so problematic, when this is how we are trained to see our relationships with other women. Hatred, sabotage and jealousy are also present in earlier tellings of the story which, though present in the current Disneyized version, is absent at its end, when Cinderella rides off into the horizon and the bad family vanishes from sight and mind. In Aschenputtel, the Grimm version of Cinderella, birds attack the evil stepsisters and bite out their eyes. But in many other accounts Cinderellas goodness is almost saintly: she forgives her stepsisters horrible behavior and sometimes even manages to match them up at court. This is certainly not what I would do—but I also have an opportunity to rewrite this story at the point of my retelling it. I have already reinterpreted the story for you using a metaphoric polemic on absence. In my story, what is most important about Cinderella is the shoe. Ways of Seeing This article concerns metaphors and ways of seeing, particularly ways of seeing what others are not looking at. The logical assumption is that a non-subject is therefore trivial, unworthy of serious study. Conversely, my response was and is to question why these are non-subjects, to investigate decisions made by others about what is likely to be important to me or to anyone else. So my work begins with a rejection—of the canon, of the politics of literature and its publication, of academic appropriateness, of the legislation of opinion. One of the ways that academics seem to operate is through the posing of binary or structural opposites. It is comforting to  know that if a thing is not this it must be that; what is not cold is hot. Never mind that we are capable of thinking about and experiencing an enormous range of temperatures, that heat is a relative term as is cold; structural opposition (Là ©vi-Straussian construction) enforces binary coding, usually with the additional motivation of fixing, or affixing, moral values. Because one is already conditioned to look at things as this or that, cold or hot, the value indicators are similarly binary: negative and positive. We need both, of course, and not only in our flashlights: polarity is a dependent relationship. But because of this tendency towards a tension of opposites, we end up limiting our transactions, our thinking, to bad and good. This is the outcome—if not the point—of childrens literature: it conditions us to distinguish bad and good, and to make a number of other associations with these terms; that which is considered good is that which beautiful, smart, nice, polite, fair or even white, obedient, tall, slim, quiet, and so forth. In fairy tales, the basis of what we now call childrens literature, a persons inner qualities are instantly discernible from external attributes. Good and bad are physiologically, physiognomically manifest: the dark little crooked old woman in black with the wart on her nose is not going to be the hero. Thus a good person is also pleasant to look at and (as we know from television) has clean clothes, fresh breath, and carefully styled hair. I have gone into an extended discussion of binarisms and ethics because I invite you to suspend binary judgements, to move beyond an evaluation of absence as the opposite of presence, and to consider absence in a different way: as something present—but not. That which is not not present is absent. When something present is not looked at, not recognized, not seen, it acquires a certain invisibility—in part, what I call absence. Absence is what is always there but overlooked, or there but unheard, or seen and heard but never mentioned. We do not immolate the story in reconsidering what it conceals. We literally unveil nothing of her, nothing that in the final account does not leave her intact, virginal (he loves only that), undecipherable, impassively tacit, in a word, sheltered from the cinder that there is and that she is (Derrida 41). 9 Those characteristics of Cinderella left un-addressed support this view of absence: somewhere behind the story sits another story, the one we are not meant to hear. Were we to hear it we would walk away with an entirely  different perception of the poor beaten Cinderella—or several different perceptions.10 We might be inspired to question the value of the hidden features, to wonder where issues of class, aesthetics, nature, superstition, parenting, hunger or politics fit in our founding myths, to wonder at the importance of such a myth as Cinderella in our female lives. We might be sufficiently moved to overturn the patriarchal texts, insert others in their place (Nature filling its vacuum). Not, that is, to rewrite Cinderella, but instead to find a more feasible model for contemporary female behavior. Perhaps even to acknowledge that there can be no models except those we embrace through personal experience. Absence is something more than its frail partner presence—a location for the political, for what is challenging for societies and social conditions, for what must not be looked at, not seen, not noted, not touched. Not presented. Absence is dangerous. To locate absence is to chart life, history, sociology, in a specific way. The Cinderella story presents an array of questionable absences, textually unanswered because unquestioned. This discussion does not pretend to provide closure, but rather to enjoin readers to ask questions of their own. Unlike other ways of seeing, this strategy does not limit or eliminate the text, but it does subvert it. By examining our essential stories, those we encountered at the knee, and those we teach to children, we begin to see in other ways, to discover culture as a tool for moral education, sexual regulation and female containment, and to locate female absence very close to home. 1I do not wish to repeat the excellent extensive historical scholarship on Cinderellas origins here. Cinderellas lengthy and interesting histories, irrelevant in this discussion, can be found in the following brief bibliography: Bruno Betelheim, The Uses of Enchantment: the Meaning and Importance of Fairy Tales (New York: Knopf, 1976); Alan Dundes, ed., Cinderelle: A Folklore Casebook (New York: Garland Pub., 1982); Walt Disney, Cinderella [Videorecording], (Burbank: Walt Disney, 1949); Nai-Tung Ting, The Cinderella Cycle in China and Indo-China (Helsinki: Suomalainen Tiedeakatemia, 1974). [ Return to the article ] 2A cursory review reveals these addenda: Colette Dowling, The Cinderella Complex: Womens Hidden Fear of Independence (New York: Summit Books, 1981); Barbara Einhorn, Cinderella Goes to Market: Citizenship, Gender, and Womens Movements in East Central Europe (London: Verso, 1993); Eugene Paul Nassar, The Rape of Cinderella: Essays In Literary Continuity (Bloomington : Indiana University Press, 1970); a curious history of something entirely other—D. C. M. (Desmond Christopher St. Martin) Platt, The Cinderella Service: British Consuls Since 1825 (Hamden, Conn: Archon Books, 1971); Cinderella considered as an anti-fairy tale in Robert Walser, Robert Walser Rediscovered: Stories, Fairy-Tale Plays, and Critical Responses, ed. Mark Harman (Hanover, NH: Published For Dartmouth College by University Press of New England, 1985); Margarita Xanthakou, Cendrillon Et Les Soeurs Cannibales: De La Stakhtobouta Maniote (Grece) A Lapproche Comparative De Lanthropophagie Intraparentale Imaginaire (Paris: Editions De Lecole Des Hautes Etudes En Sciences Sociales, 1988). For a subversive and extensive recovery of what cinder (cendre) is (or to what cinder is reduced/reducible), see Jacques Derrida, Cinders, ed. and trans. Ned Lukacher (Lincoln: University of Nebraska Press, 1991). [ Return to the article ] 3Rodgers and Hammersteins music backed a movie produced as a musical in the same year: Richard Rodgers and Oscar Hammerstein, Cinderella [Videorecording] (Hollywood: Samuel Goldwyn Company, 1964). [ Return to the article ] 4Mallarmà ©, Oeuvres Completes, Plà ©iade edition (Paris: Gallimard, 1945) 3-4. [ Return to the article ] 5It would be difficult to ascertain where the fable had its first expression, as scholars trace it to Germany, France and even China; a student tells me of the Hungarian version, in which the young woman is named Hamupipoke, and her shoes, curiously enough, are made of white diamonds. The symbolism could not be clearer. On form and structure, see also Vladimir Propp, The Morphology of the Folktale. Translated by Laurence Scott (Austin: University of Texas Press, 1968). [ Return to the article ] 6This is given greater consideration in my article Travesty, Peterhood, The Flight of a Lost Girl, New England Review, forthcoming (August 1988). James M. Barrie also wrote a play named Cinderella not very surprising in view of the fairytale quality of Peter Pan and many of his other writings. [ Return to the article ] 7One of the few exceptions is Mary Poppins, who is also depicted as an aberrant, desexualized creature. For one thing, she is a woman without children of her own, who literally takes, and seduces, other peoples children. Here again is a magical woman, a witch, dressed in black, like a widow; appropriately,  her boyfriend is also a witch of sorts, having the luck of the chimneysweeps. Does it not seem curious to anyone that he is able to impart good fortune through physical contact—and is this not somehow frightening? (As parents wouldnt you tell your children, Just say no?) Marys relationship with Bert does not stray from what we expect, even demand, of her class—her boyfriend (neither is married, nor do they discuss it, at least onscreen) is also a working-class Victorian London stiff (which is to say that he is also poor), with the robust happiness we need to ascribe to poor people, as well as a tendency to copulate below stairs; still we never see or are even permitted to imagine the content of their romantic holidays, interrupted by a song or some bit of magic. Because of her magic, and an understanding of what children really need that surpasses the ordinary, Mary is cleverly depicted as being able to breach the class zone: here her magic characteristics are essential for an explanation of this otherwise scandalous, and (in terms of class distinctions) uncomfortable flexibility. She doesnt know her place—the moral that the childrens father ends in teaching, as he rescues his children from the unsavoriness of their relationship with this queerly unmarried woman and her odd friend. Marys ability to tread between classes, however, elevates her even from Berts league: we know that she will leave him too, and are secretly satisfied. He is, for one thing, truly from the lowest class, as his mangled Cockney accent tells us, while Marys impossibly perfect speech distinguishes her as something quite different (though this is never really acknowledged); Bert is also, if only figuratively, black, while Mary is, however trenchantly, white. [ Return to the article ] 8The modern movie Ace Ventura, Pet Detective contains a wonderful quotation of a scene from Disneys Snow White. Actor Jim Carrey stands in the center of a room and the animals fly, run, walk, creep and slither to him as he belts out a high note. [ Return to the article ] 9I have re-rendered the parenthetical phrase (only), which Ned Lukacher translates as thats the only thing he loves, because of its (increased) ambiguity in the context of a feminist reading. [ Return to the article ] 10In her book Cinderella on the Ball: Fairytales for Feminists (Dublin: Attic Press, 1991), editor Margaret Neylon offers re-readings of the classic folktales. In the Cinderella story, it is the two sisters who emerge supreme: ugliness is a cover for intelligence and political feminism. [ Return to the article ]

Measures of Central Tendency

Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is Measures of Central Tendency Measures of Central Tendency The one single value that reflects the nature and characteristics of the entire given data is called as central value. Central tendency refers to the middle point of a given distribution. It is other wise called as ‘measures of location. The nature of this value is such that it always lies between the highest value and the lowest value of that series. In other wards, it lies at the centre or at the middle of the series. CHARACTERISTICS OF A GOOD AVERAGE: Yule and Kendall have pointed out some basic characteristics which an average should satisfy to call it as good average. They are: Average is the easiest method to calculate It should be rigidly defined. This says that, the series of whose average is calculated should have only one interpretation. One interpretation will avoid personal prejudice or bias. It should be representative of the entire series. In other wards, the value should lie between the upper and lower limit of the data. It should have capable of further algebraic treatment. In other wards, an ideal average is one which can be used for further statistical calculations. It should not be affected by the extreme values of the observation or series. DEFINITIONS: Different experts have defined differently to the concept of average. Gupta (2008) in his work has narrated Lawrence J. Kaplan definition as ‘one of the most widely used set of summery figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose of computing an average value for a set of observation is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point of location around which the individual items cluster. This opinion clearly narrates the basic purpose of computing an average. Similarly, Croxton and Cowden define the concept as ‘an average is a single value within the range of the data that is used to represent all of the values in the series. Since the average is somewhere within the range of data, it is sometimes called a measure of central value. TYPES OF AVERAGES: Following five are frequently used types of an average or measure of central tendency. They are Arithmetic mean Weighted arithmetic mean Median Mode Geometric Mean and Harmonic Mean All the above five types are discussed below in detail. THE ARITHMETIC MEAN: Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. It can be computed in a several ways. Commonly it can be computed by dividing the total value by the number of observations. Let ‘n be the number of items in a case. Each individual item in a list can be represented in a relationship as x1, x2, x3, ,xn. In this relationship, ‘x1 is one value, ‘x2 is another value in the series and the value extends upto a particular limit represented by ‘xn. The dots in the relationship express that there are some values between the two extremes which are omitted in the relationship. Some people interprets the same relationship as, which can be read as ‘x-sub-i, as i runs from 1 upto n. In case the numbers of variable in list is more, then it requires a long space for deriving the mean. Thus the summation notation is used to describe the entire relationship. The above relationship can be derived with the help of summation as: , representing the sum of the ‘x values, using the index ‘i to enumerate from the starting value i =1 to the ending value i = n. thus we have and the average can be represented as The symbol ‘i is again nothing but a continuing covariance. The readers should not be confused while using the notation , rather they can also use or or any other similar notation which are of same meaning. The mean of a series can be calculated in a number of ways. Following are some basic ways that are commonly used in researchers related to management and social sciences, particularly by the beginners. However, the readers should not be confused on sample mean and population mean. A sample of a population of ‘n observations and the mean of sample is denoted by ‘. Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol ‘Â µ, which is pronounced as ‘mue and is derived from the Greek letter ‘mu. Below we are discussing the concepts of sample mean. Type-1: In case of individual observation: a. Direct method- Mean or average can be calculated directly in the following way Step-1: First of all the researcher has to add all the observations of a given series. The observations are x1, x2, x3, xn. Step-2- Count how many observations are their in that series (n) Step-3- the following procedure than adopted to get the average. Thus the average or mean denoted as ‘and can be read as ‘x bar is derives as: Thus it can be said that the average mark of the final contestants in the quiz competition is 67.6 marks which can be rounded over to 70 marks. b. Short-cut method- The average or mean can also be calculated by using short-cut method. This method is applicable when a particular series is having so many observations. In other wards, to reduce calculations this method is generally used. The steps of calculating mean by this method is as follows: i. The research has to assume any one value from the entire series. This value is called as assumed value. Let this value be denoted here as ‘P. ii. Differentiate each a value from this assumed vale. That is find out individual values of each observation. Let this difference value be denoted as ‘B. Hence B=xn-P where n= 1,2,3,n. iii. Add all the difference value or get sum of B and count the number of observation ‘n. iv. Putting the values in the following formula and get the value of mean. Type-2: In case of discrete observations or series of data: Discrete series are the variables whose values can be identified and isolated. In such a case the variant is a whole number, but is form frequency distribution. The data set derived in case-1 above is called as ungrouped data. The computations in case of these data are not difficult. Where as, if the data set is having frequencies are called as groped data. a. Direct method: Following are some steps of calculating mean by using the direct method i. In the first step, the values of each row (X) are to be multiplied by its respective frequencies (f). ii. Calculate the sum of the frequencies (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*f values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula b. Short cut method: Arithmetic mean can also be calculated by using the short cut method or assumed mean method. This method is generally used by the researchers to avoid the time requirements and calculation complexities. Following are the steps of calculating mean by this method. i. The first step is to assume a value from the ‘X values of the series (denoted as A= assumed value) ii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘X to that of assumed value (A) i.e., D = X-A iii. Multiply each D with f i.e., find our Df iv. Calculate the value of sum of at the end of respective columns. v. Mean can be calculated by using the formula as Type-3: In case of continuous observations or series of data: Another type of frequency distributions is there which consists of data that are grouped by classes. In such case each value of an observation falls somewhere in one of the classes. Calculation of arithmetic mean in case of grouped data is some what different from that of ungrouped data. To find out the arithmetic mean of continuous series, one has to calculate the midpoint of each class interval. To make midpoints come out in whole cents, one has to round up the value. Mean in continuous series can be calculated in two ways as derived below: a. Direct method: In this method, mean can be calculated by using the steps as i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Multiply the mid points of each class interval (m) with its respective frequencies (f) i.e., find out mf iii. Calculate the value of sum of at the end of respective columns. iv. Mean can be calculated by using the formula as b. Short cut method: Mean can also be calculated by using short cut method. Following are the steps to calculate mean by this method. i. First step is to calculate the mid point of each class interval. The mid point is denoted by ‘m and can be calculated as . ii. Assume a value from the ‘m values of the series (denoted as A= assumed value) iii. In this step in another column we have to calculate the deviation value (denoted as D) of ‘m to that of assumed value (A) i.e., D = m A iv. Multiply each D with f i.e., find our Df v. Calculate the value of sum of at the end of respective columns. vi. Put the values in the following formula to get mean of the series THE WEIGHTED ARITHMETIC MEAN: In real life situation in management studies and social sciences, some items need more importance than that of the other items of that series. Hence, importance assigned to different items with the help of numerical value as per the priority basis in a series as called as weights. The arithmetic mean on the other hand, gives equal weightage or importance to each observation of the series. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. Following is the procedures of computing mean of a weighted series. By the way, an important problem that arises while using weighted mean is regarding selection of weights. Weights may be either actual or arbitrary, i.e., estimated. The researcher will not face any difficulty, if the actual weights are assigned to the set of data. But in case, if actual data is not assigned than it is advisable to assign arbitrary or imaginary weights. Following are some steps of calculating weighted mean: i. In the first step, the values of each row (X) are to be multiplied by its respective weights (W) ii. Calculate the sum of the weights (column-2 in our example) at the end of the column denoted as iii. Calculate the sum of the X*W values at the end of the column (column-3 in our below derived example) denoted as iv. Mean () can be calculated by using the formula Advantages of Arithmetic mean: Following are some advantages of arithmetic mean. i. The concept is more familiar concept among the people. It is unique because each data set has only one mean. ii. It is very easy to compute and requires fewer calculations. As every data set has a mean, hence, as a measure mean can be calculated. iii. Mean represents a single value to the entire data set. Thus easily one can interpret a data set its characteristics. iv. An average can be calculated of any type of series. Disadvantages of Arithmetic mean: The disadvantages are as follows. i. One of the greatest disadvantages of average is that it is mostly affected by the extreme values. For example let consider Sachin Tendulkars score in last three matches. Let it be, 100 in first match, 2 in second match and 10 in third match. The average score of these three matches will me 100+2+10/3=37. Thus it implies that Tendulkars average score is 37 which is not correct. Hence lead to wrong conclusion. ii. It is not possible to compute mean for a data set that has open-ended classes at either the high or low end of the scale. iii. The arithmetic average sometimes gives such value which cannot be found from the data series from which it is calculated. iv. It is unrealistic. v. It cannot be identified observation or graphic method of representing the data and interpretation. THE MEDIAN: Another one technique to measure central tendency of a series of observation is the median. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. In other wards, it is the exactly middle value of the series. Hence, fifty percent of the observations in the series are above the median value and other fifty or half observations are remains below the median value. However, if the series are having odd numbers of observations like 3,5,7,9,11,13 etc., then the median value will be equal to one of the exact value from the series. On the other hand, if the series is having even observations, then median value can be calculated by getting the arithmetic mean of the two middle values of the observations of the series. Median an a technique of measuring central tendency can be best used in cases where the problem sought for more qualitative or psychological in nature such as health, intelligence, satisfaction etc. Definitions: The concept of median can be clearer from the definitions derived below. Connor defined it as ‘the median is the value which divides the distribution into two equal parts, one part comprising all values greater, and the other values less than the median. Where as Croxton and Cowden defined it as ‘the median is that value which divides a series so that one half or more of the items are equal to or less than it and one half or more of the items are equal to or greater than it. Median can be computed in three different series separately. All the cases are discussed separately below. Computation of Median in Individual Series Computation of Median in Discrete Series and Computation of Median in Continuous Series Computation of Median in Individual Series: Following are some steps to calculate the median in individual series. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. Than the median value can be calculated by using the formula th value or item from the series. Where, N= Number of observation in that series. When N is odd number (like 5, 7,9,11,13 etc.) median value is one of the item within that series, but in case N will be a even number than median is the arithmetic mean of the two middle value after applying the above formula. The following problem can make the concept clear. Computation of Median in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Following are the steps of computing the median when the series is discrete. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies of the series. Computation of Median in Continuous Series: Continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of median is little bit different from that of the other two cases discussed above. Following are some steps to get median in continuous series of data. The first and the most important requirement is that the data should be arranged in an ascending (increasing) or descending (decreasing) order. In the third column of the table, calculate the cumulative frequencies. Than the median class can be calculated by using the formula th value or item from the cumulative frequencies column of the series. Form the cumulative frequencies, one can get the median class i.e., in which class the value lies. This class is called as median class and one can get the lower value of the class and the upper value of the class. The following formula can be used to calculate the median We have to get the median class first. For this, median class is N/2 th value or 70/2= 35. The value 35 lies in the third row of the table against the class 30-40. Thus 30-40 is the median class and it shows that the median value lies in this class only. After getting the median class, to get the median value we have to apply the formula . Advantages of Median: Median as a measure of central tendency has following advantages of its own. It is very simple and can be easily understood. It is very easy to calculate and interpret. It Includes all the observations while calculation. Like that of arithmetic mean, median is not affected by the extreme values of the observation. It has the advantages for using further analysis. It can even used to calculate for open ended distribution. Disadvantages of Median: Median as a means to calculate central tendency is also not free from draw backs. Following are some important draw backs that are leveled against median. Median is not a widely measure to calculate central tendency like that of arithmetic mean and also mode. It is not based on algebraic treatment. THE MODE: Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. Like that of median, mode is also more useful in case of qualitative data analysis. It can be used in problems generally having the discrete series of data and particularly, problems involving the expression of psychological determinants. Definitions: The concept of mode can be clearer from the definitions derived below. Croxten and Cowden defined it as ‘the mode of a distribution is the value at the point around which the items tend to be most heavily concentrated. It may be regarded as the most typical of a series of value. Similarly, in the words of Prof. Kenny ‘the value of the variable which occurs most frequently in a distribution is called the mode. Mode can be computed in three different series separately. All the cases are discussed separately below. Computation of Mode in Individual Series Computation of Mode in Discrete Series and Computation of Mode in Continuous Series Computation of Mode in Individual Series: Calculation of mode in individual series is very easy. The data is to be arranged in a sequential order and that value which occurs maximum times in that series is the value mode. The following example will make the concept clear. Computation of Mode in Discrete Series: Discrete series are those where the data set is assigned with frequencies or repetitions. Hence directly, mode will be that value which is having maximum frequency. By the way, for accuracy in calculation, there is a method called as groping method which is frequently used for calculating mode. Following is the illustration to calculate mode of a series by using grouping method. Consider the following data set and calculate mode by using the grouping method. The calculation carried out in different steps is derived as: Step-1: Sum of two frequencies including the first one i.e., 1+2=3, then 4+3=7, then 2+1=3 etc. Step-2: Sum of two frequencies excluding the first one i.e., 2+4=7, then 3+2=5, then 1+2=3 etc. Step-3: Sum of three frequencies including the first one i.e., 1+2+4=7, then 3+2+1=6 etc. Step-4: Sum of two frequencies excluding the first one i.e., 2+4+3=9, then 2+1+2=5 etc. Step-5: Sum of three frequencies excluding the first and second i.e., 4+3+2=9, then 1+2+1=4. Computation of Mode in Continuous Series: As already discussed, continuous series are the series of data where the data ranges are in class intervals. Each class is having an upper limit and a lower limit. In such cases the computation of mode is little bit different from that of the other two cases discussed above. Following are some steps to get mode in continuous series of data. Select the mode class. A mode class can be selected by selecting the highest frequency size. Mode value can be calculated by using the following formula Advantages of Mode: Following are some important advantages of mode as a measure of central tendency. It is easy to calculate and easy to understand. It eliminates the impact of extreme values. It is easy to locate and in some cases we can estimate mode by mere inspection. It is not affected by extreme values. Disadvantages of Mode: Following are some important disadvantages of mode. It is not suitable for further mathematical treatment. It may lead to a wrong conclusion. Some critiques criticized mode by saying that mode is influenced by length of the class interval. THE GEOMETRIC MEAN: Geometric mean, as another measure of central tendency is very much useful in social science and business related problems. It is an average which is most suitable when large weights have to be assigned to small values of observations and small weights to large values of observation. Geometric mean best suits to the problems where a particular situation changes over time in percentage terms. Hence it is basically used to find the average percent increase or decrease in sales, production, population etc. Again it is also considered to be the best average in the construction of index numbers. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. For example, if a series is having only two observations then N will be two or we will take square root of the observations. Similarly, when series is having three observations then we have to take cube root and the process will continue like wise. Geometric mean can be calculated separately for two sets of data. Both are discussed below. When the data is ungrouped: In case of ungrouped series of observations, GM can be calculated by using the following formula: where X1 , X2 , X3, XN various observations of a series and N is the Nth observation of the data. But it is very difficult to calculate GM by using the above formula. Hence the above formula needs to be simplified. To simplify the formula, both side of the above formula is to be taken logarithms. To calculate the G.M. of an ungrouped data, following steps are to be adopted. Take the log of individual observations i.e., calculate log X. Make the sum of all log X values i.e., calculate Then use the above formula to calculate the G.M. of the series. When the data is grouped: Calculation of geometric mean in case of grouped data is little bit different from that of calculation of G.M. in case of ungrouped series. Following are some steps to calculate the G.M. in case of grouped data series. To calculate the G.M. of a grouped data, following steps are to be adopted. Take the mid point of the continuous series. Take the log of mid points i.e., calculate log X and it can also be denoted as log m Make the sum of all log X values i.e., calculate or Then use the following formula to calculate the G.M. of the series. Advantages of G.M.: Following are some advantages of G.M. i. One of the greatest advantages of G.M. is that it can be possible for further algebraic treatment i.e., combined G.M., can be calculated when there is availability of G.M., of two or more series along with their corresponding number of observations. ii. It is a very useful method of getting average when the series of observation possess rates of growth i.e., increase or decrease over a period of time. iii. Since it is useful in averaging ratios and percentages, hence, are more useful in social science and business related problems. Disadvantages of G.M.: G.M., as a technique of calculating central value is also not free from defects. Following are some disadvantages of G.M. i. It is very difficult to calculate the value of log and antilog and hence, compared to other methods of central tendency, G.M., is very difficult to compute. ii. The greatest disadvantage of G.M., is that it cannot be used when the series is having both negative or positive observations and observations having more zero values. THE HARMONIC MEAN: The last technique of getting the central tendency of a series of data is the Harmonic mean (H.M.). Harmonic mean, like the other methods of central tendency is not clearly defined. It is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. H.M., is very much useful in those cases of observations where the nature of data is such that it express the average rate of growth of any events. For example, the average rate of increase of sales or profits, the average speed of a train or bus or a journey can be completed etc. Following is the general formula to calculate H.M.: When the data is ungrouped: When the observations of the series are ungrouped, H.M., can be calculated as: The step for calculating H.M., of ungrouped data by using the derived formula is very simple. In such a case, one has to find out the values of 1/X and then sum of 1/X. When the data is grouped: In case of grouped data, the formula for calculating H.M., is discussed as below: Take the mid point of the continuous series. Calculate 1/X and it can also be denoted as 1/m Make the sum of all 1/X values i.e., calculate Then use the following formula to calculate the H.M. of the series. Advantages of H.M.: Harmonic mean as a measure of central tendency is having following advantages. i. Harmonic mean considers each and every observation of the series. ii. It is simple to compute when compared to G.M. iii. It is very useful for averaging rates. Disadvantages of H.M.: Following are some disadvantages of H.M. i. It is rarely used as a technique of measuring central tendency. ii. It is not defined clearly like that of other techniques of measuring central value mean, median and mode. iii. Like that of G.M., H.M., cannot be used when the series is having both negative or positive observations and observations having more zero values. CONCLUSION: An average is a single value representing a group of values. Each type of averages has their own advantages and disadvantages and hence, they are having their own usefulness. But it is always confusing among the researchers that which average is the best among the five different techniques that we have discussed above? The answer to this question is very simple and says that no single average can be considered as best for all types of data. However, experts opine two considerations that the researchers must be kept in mind while going for selecting a technique to determine the average. The first consideration is that of determining the nature of data. If the data is more skewed it is better to avoid arithmetic mean, if the data is having gap around the middle value of the series, then median should be avoided and on the other hand, if the nature of series is such that they are unequal in class-intervals, then mode is to be avoided. The second consideration is on the type of value req uired. When there is need of composite average of all absolute or relative values, then arithmetic mean or geometric mean is to be selected, in case the researcher is in need of a middle value of the series, then median may be the best choice, but in case the most common value is needed, then will not be any alternative except mode. Similarly, Harmonic mean is useful in averaging ratios and percentages. SUMMERY: 1. Different experts have defined differently to the concept of average. 2. Arithmetic mean is the most simple and frequently used technique of computing central tendency. The average is also called as mean. It is other wise called as a single number representing a whole data set. 3. The best use of arithmetic mean is at the time of correcting some wrong entered data. For example in a group of 10 students, scoring an average of 60 marks, in a paper it was wrongly marked 70 instead of 65. the solution in such a cases is derived below: 4. In such a case, the weighted mean acts as the most important tool for studying the behaviour of the entire set of study. Here use of weighted mean is the only measure of central tendency for getting correct and accurate result. 5. Median is generally that value of the entire series which divides the entire series into two equal parts from the middle. 6. Mode is defined as the value which occurs most often in the series or other wise called as the value having the highest frequencies. It is, hence, the value which has maximum concentration around it. 7. Geometric mean is defined as the Nth root of the product where there are N observations of a given series of data. 8. Harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the individual observations. QUESTIONS: 1. In a class containing 90 students following heights (in inches) has been observed. Based on the data calculate the mean, median and mode of the class. 2. In a physical test camp meant for selection of army solders the following heights of the candidates have been observed. Find the mean, median and mode of the distribution. 3. From the distribution derived below, calculate mean and standard deviation of the series. 4. The following table derives the marks obtained in Indian Economy paper by 90 students in a class. Calculate the mean, median and mode of the following distribution. 5. The monthly profits of 180 shop keepers selling different commodities in a city footpath is derived below. Calculate the mean and median of the distribution. 6. The daily wage of 130 labourers working in a cotton mill in Ahmadabad cith is derived below. Calculate the mean, median and mode. 7. There is always controversy before the BCCI before selection of batsmen between Rahul Dravid and V.V.S. Laxman. Runs of 10 test matches of both the players are given below. Suggest who the better run getter is and who the consistent player is. 8. Calculate the mean, median and mode of the following distribution. 9. What do you mean by measure of central tendency? How far it helpful to a decision-maker in the process of decision making? 10. Define measure of central tendency? What are the basic criteria of a good average? 11. What do you mean by measure of central tendency? Compare and contrast arithmetic mean, median and mode by pointing out the advantages and disadvantages. 12. The expenditure on purchase of snacks by a group of hosteller per week is