Intelligence failure is political and psychological organisation

Intelligence failure is political and psychological organisation Intelligence failure is political and psychological more often than organisational. Discuss in relation to at least two examples of intelligence failure. In this essay I will illustrate, through specific examples, the human condition and the psychological roots of surprise, the actions of policy-makers and an examination of organisational defects of agencies, and how they contribute to intelligence failures. However in order to understand what constitutes ‘intelligence failure, some contextual definition must be provided. The phrase intelligence failure often has highly negative connotations in terms of national security. Although it is also been used to describe situations such as the 1998 Indian nuclear weapons tests whereby U.S and Western policy-makers were surprised by the international incident that took place, even when that surprise caused minimal impact to their national security. Using the word failure to describe situations where negative consequences for national security are minimal may seem unusual however it highlights the imprecise meaning of the word. The amassing of, interpretation and eventual distribution of information to those in power is an ongoing process that can occasionally fail to depict events on the international scene accurately or adequately in-depth to provide them with either infallible information or total certainty.As a result, when surprises like Pearl Harbour and the 9/11 attacks occur, intelligence agencies bear the brunt of the scrutiny. It is interesting to no te that in a study conducted by Dr. Robert Johnston within the U.S. Intelligence Community in 2005 he interviewed several CIA officials and requested a definition of the term ‘intelligence failure from several of the interviewees. Some of the responses disavowed the existence of ‘intelligence failure while others placed the terms in the broader context of policy and decision making. It is apparent that one of the most difficult elements in intelligence analysis rests in measuring up enemy intention and removing the element of surprise. Surprise is essentially a psychological phenomenon that has its roots in human nature.This process is not made any easier if the intelligence gathered is unreliable, incomplete or just plain absent. Furthermore, knowledge about capability does not supply a perfect clue to intentionas will be demonstrated below. A common failing is to create an interpretation of the enemys intentions yet base it on the ideology or belief of the analyst and his home nation. Hindsight reveals that the element of surprise in the majority of large-scale wars fought since 1939 was unwarranted and a considerable amount of evidence of an imminent assault was available to the victims before the fact. In 1941 a number of high ranking administration officials expressed the belief that as long as the U.S maintained overall military advantage over Japan, war was unlikely to break out. All the evidence indicates that they are more afraid of war with the U.S. than anything else. U.S policy-makers remained firm in their belief that Japan would base its decision to wage war on military considerations. It has been argued that, as Japanese/U.S. relations were on a steady decline and with a large number of reports being received regarding possible Japanese aggression and aggressive intentions, U.S. officials had almost certain knowledge that war was at hand. Roberta Wohlstetter attributes the failure to anticipate the attack on Pearl Harbour on the massive number of irrelevant material being accumulated regarding Japanese intentions, euphemistically termed ‘noise. In addition, not all intercepts were decoded and the intercepts that were, did not all travel along the same communication routes and so ended up not rising the chain of command; no single person or agency ever had at any given moment all the signals existing in this vast information network. Wohlstetter also believes that intelligence officers could perhaps have foreseen the attack years before, if the U.S. had concealed spies within Japanese military circles and expanded its code-breaking capabilities. Of course, it can be further argued that success in warning can be indistinguishable from failure. If, for example, the defender acknowledges a warning and responds in time with defensive preparations then the attacker may cancel the operation. Thus the original prediction would be rendered invalid. The Japanese task force en route to Pearl Harbour had orders to abort if the element of surprise was lost. During the week preceding the Yom Kippur war, Israeli intelligence officers accumulated a substantial amount of credible information indicating unusual Egyptian activities along the Suez Canal. A memorandum was circulated to Intelligence Command which concluded that there was a high probability that Egyptian manoeuvres were only cover for an impending attack. The intelligence indicated a readiness for an offensive however on the eve of war; the intelligence material did not affect the strategic thinking of Israelis decision makers. They attributed their own line of reasoning to the adversary. Overlooking the possibility that the enemy might not follow the same line of thought the Israeli leaders displayed a fatal lack of imagination that separated them from their opponent and in this case, aided by hindsight, it is clear that when tactical facts differ from that of strategic possibilities, the former should be given increased weight in the decision making process. As established above, the cause of intelligence failure can be a result of an analysts own psychological condition influencing data, reports or opinions of others, likewise policymakers can be guilty of the same. In this next example I will demonstrate how not only the psychological condition can result in an intelligence failure. Since the 9/11 disaster public discussion has been focused strongly on the human causes of the tragedy and asking the question ‘What went wrong? And one of the failures of the intelligence community that had been overlooked in the beginning was the organisational structure of both the FBI and CIA. On closer examination, it is evident that the Bureau and CIA suffered from a litany of organisational weaknesses that can be attributed to being a major component of the 9/11 disaster. The structural problems the FBI faced were exacerbated by the fact the bureau was part of an Intelligence Community that had been be in opposition to information sharing, the CIA and FBI having a long history of poor communication added to divided responsibility geographically which invariably led to vast gaps in coverage of territory. Whilst the CIA was among the agencies charged with tracking terrorists abroad, the FBI had responsibility for monitoring terrorist suspects within U.S borders. There was however no clear distinction of responsibility for monitoring movement of terrorist suspects between the U.S and foreign countries. The bureau was considered so peripheral that previous to 9/11 the CIA neglected to put the Attorney General on its distribution list for the Presidents Daily Brief, the most important Community-wide current intelligence report. Consequently, terrorists could operate freely across borders but the U.S Intelligence Community could not. Whats more, J. Edgar Hoover had created a specific picture of FBI agents in a large publicity campaign that soon agents themselves began believing; they were glorified agents, in everything from movies to play cards with the ultimate goal for a striving ambitious agent was to work criminal cases and not sit behind a desk, and so this had an unfortunate side effect an aversion to technology and analysis. As one agents describes the ‘old-school mentality after the 9/11 attacks, ‘real men dont type. The only thing a real agent needs is a notebook, a pen and a gun, and with those three things you can conquer the world. With that perspective in mind, greater emphasis was placed on the more tangible criminal conviction, as opposed to a very absent terrorist attack. To further the argument, organisational incentives supplemented this way of thinking with opportunities for analysts promotion to senior positions highly restricted if permitted at all. Moreover, in terms of techno logy, the FBI computer system was so outmoded that it took up to 12 commands to store a single document, this coupled with an almost pathological distain for counterintelligence operations meant that billions of records were simply kept in paper files in shoe boxes and if reports did come in, they were not assigned a high priority level. The CIA also suffered from similar failings in its internal structure. When the organisation was created, it was charged with conducting missions to collect covert intelligence, engage in covert action and it also publishes National Intelligence Estimates (NIE). Thus in similar fashion to the FBI ‘bi-polarity of having duel missions law enforcement and intelligence- these tasks cannot be suitably carried out and the intelligence analysis can end up politicised. The CIA had not been particularly strong on terrorism since the late 1980s. William Casey and Robert Gates Director and deputy director respectively falsely believed that the Soviet Union was responsible for every act of international terrorism and formed the Counter-terrorism Centre (CTC). Even after the failed plot to bomb Los Angeles International Airport in December 1999, the agencies did not heighten concerns over the ability of Al-Qaeda to strike inside the U.S. Everyone has someone they want to hold responsible for 9/11 and although different people have found different culprits, their point is the same: that individual leaders are to blame for the World Trade Centre and Pentagon attacks. It is however, dangerous to place the entire burden of responsibility on single individuals, though it may be understandable, as it is a natural human response after a great tragedy. It does however suggest the wrong causes of failure and thus the wrong remedies in tackling them. For instance, well-meaning ‘intelligence reform advocates including members of Congress and families, of 9/11 victims mistakenly fixed their sights on measure recommended by the 9/11 Commission, most notably the creation of the Director of National Intelligence (DNI). It would be ridiculous to say that individual leadership is irrelevant; it would merely be more prudent to examine the less noticeable aspects of organisational life. If it was the case that leadership determin ed counterterrorism success and failure, then resolution to the problems encountered by the intelligence agencies would be easy. To conclude, it seems that the enduring defects in the FBI and CIA organisational structure, culture, and incentive systems proved to be a major debilitating factor once the Cold War was over and the terrorist threat emerged. These weaknesses ultimately prevented the agencies from exploiting 12 separate opportunities that might have disrupted the 9/11 plot. These agencies may be charged with preventing surprise but not all surprises can be prevented, such as the abrupt end of the Cold War and collapse of the Soviet Union. Furthermore it seems the danger of defining ‘intelligence failure by example resembling those above is that each case is contextually unique and can be argued with no end in sight. The important recurring element through the examples illustrated is the significance of surprise, regardless of if it is intelligence surprise, military surprise in the case of Pearl Harbour and the Yom Kippur war, or political surprise. Even if the intelligence community itself was not surprised by them, it was unable to convince the military and political consumers of intelligence, these events might occur; in which case it suggests the failure is one of organisational and specifically of communication and persuasion. Marrin, S., ‘Preventing Intelligence Failure by Learning from the Past International Journal of Intelligence and Counterintelligence 17/4 (2004) p. 657 Marrin, S., ‘Preventing p.656 Johnson, R. Analytic Culture in the US Intelligence Community: An Ethnographic Study (Centre for the Study of Intelligence 2005) ch. 1- https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/analytic-culture-in-the-u-s-intelligence-community/full_title_page.htm (accessed 18th March 2010). Harkabi, Y., Nuclear War and Nuclear Peace (Jerusalem: Israel Program for Scientific Translations, 1966) p. 51 Kennan, G. F., Russia, The Atom and the West (New York 1957) p. 21 Betts, R. K., ‘Surprise Despite Warning: Why Sudden Attacks Succeed Political Science Quarterly 95/4 (1980) p. 551 Letter sent by Stimson to the New York Times February 11th 1940 Ben-Zvi, A, ‘Hindsight and Foresight: A Conceptual Framework for the Analysis of Surprise Attacks World Politics 28/3 (April 1976) p. 389 Wohlstetter, R., Pearl Harbour: Warning and Decision (Stanford University Press 1962) p. 385 Wohlstetter, R., Pearl Harbour p. 193 Shlaim, A., ‘Failures in National Intelligence Estimates: The Case of the Yom Kippur War World Politics 28/3 (April 1976) p. 378 Betts, R.K., ‘Surprise Despite Warning p. 557 Ben-Zvi, A, ‘Hindsight and Foresight p. 393 Schiff, Z., October Earthquake Yom Kippur 1973 (Tel-Aviv: University Publishing Projects 1974) p. 27 Shlaim, A., ‘Failures in National Intelligence Estimates p. 363 Shlaim, A., ‘Failures in National Intelligence Estimates p. 395 Goodman, M.A., ‘9/11: The Failure of Strategic Intelligence Intelligence and National Security 18/4 (2003) p. 64 ‘Threats and Responses in 2001 9/11 Commission Staff Statement Number 10 (13th April 2004) p. 5 Zegart, A. ‘9/11 and the FBI: The Organisational Roots of Failure Intelligence and National Security 22/2 (April 2007) p. 167 Lichtblau, E. Piller, C. ‘Without a Clue: How the FBI Lost Its Way, Milwaukee Journal Sentinel, (11th August 2002) p. 1 Cumming, A. Masse, T. ‘FBI Intelligence Reform Since September 11 2001: Issues and Options for Congress Congressional Research Service Report No. RL32336 (6th April 2004) http://www.fas.org/irp/crs/RL32336.html (accessed 17th March 2010) p. 13 Federal Bureau of Investigation, ‘The FBIs Counterterrorism Program Since September 2001 Report to the National Commission on Terrorist Attacks Upon the US (14 April 2004) p.51 Goodman, M.A., ‘9/11: The Failure of Strategic Intelligence p. 62 TRACES OF TERROR: THE INTELLIGENCE AGENCIES; C.I.A.s Inquiry On Qaeda Aide Seen as Flawed New York Times 23rd September 1998 p. 11 Russell, R.L., ‘A Weak Pillar for American National Security: The CIAs Dismal Performance against WMD Threats, Intelligence and National Security 23/3 (September 2005) p. 478 Zegart, A. ‘9/11 and the FBI p. 179 Zegart, A. ‘9/11 and the FBI p. 165 Treverton, G. J., Reshaping National Intelligence for an Age of Information (New York Cambridge University Press 2003) p. 32

Mother’s love Essay

The relationship of a daughter and mother who is kindhearted and caring towards her daughter is one of the most valuable person a child has and should take for granted. In the short story by Anna Quindlen called â€Å"Mothers† is about a nineteen year old girl who her name was never mentioned in the story. The narrative has lost her mother and is trying to accept the reality that she is gone. The nineteen-year-old girl describes her life situation as if her mother was still alive, mentioning, â€Å"taking care of the wedding arrangements, or come and stay for a week after the children were born.† The young girl is conflicted over the thought of fantasies and reality, realizing that if her mother were still alive she would have strongly bonded with her and value every single moment. The short story begins with the nineteen-year-old girl, observing two women at a corner table in the restaurant. It was an older woman with her daughter spending quality time. The narrative d escribed her-self as â€Å"kind of vest pocket†, meaning she emotional feels empty and is stuck with no were to go. The narrative was wishing she had valued that moment with her mother when she had that opportunity. The girl seemed that she holds a regret inside of her because she did not have a good relationship with her mother.

The Write My Research Proposal Game

The Write My Research Proposal Game Unfortunately, there aren't any hard and fast rules on the best way to frame your research question just because there is no prescription on the best way to compose an interesting and informative opening paragraph. It's always simpler to choose one in case you have a list of proposal topics to browse. The objective of proposal writing is to persuade others your topic has to be investigated. You have to fill the template in such a manner your ideas still be in linear purchase. As you examine one research proposal example after another, you will observe the type of the paper differs on the kind of coursework regarding the paper in question. So it is necessary to communicate as a way to compose a paper that's original as if written by you. Even should you need to purchase research paper done in 6 hours, you can rely on us. 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Many students don't know how to compose a fantastic research proposal and think that it's close to writing a research paper itself. Normally, a research proposal should contain all the important elements involved with the research procedure and include sufficient information for those readers to rate the proposed study. Writing a research proposal is a lot simpler than you think and moreover it does not need any research results before you begin writing. Life, Death, and Write My Research Proposal You're doing your best, but the outcomes are sometimes not satisfying. Specify the question your research will answer, establish why it's a considerable question, show how you're likely to answer the question, and indicate what you expect we'll learn. What you're trying to explain and why, along with some feeling of the variety of variation in the dependent variable. 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Measures of central tendency - Free Essay Example

Sample details Pages: 21 Words: 6267 Downloads: 5 Date added: 2017/06/26 Category Statistics Essay Did you like this example? 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 à ¢Ã¢â€š ¬Ã‹Å"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: Don’t waste time! Our writers will create an original "Measures of central tendency" essay for you Create order 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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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, à ¢Ã¢â€š ¬Ã‹Å"x1 is one value, à ¢Ã¢â€š ¬Ã‹Å"x2 is another value in the series and the value extends upto a particular limit represented by à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"x values, using the index à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"n observations and the mean of sample is denoted by à ¢Ã¢â€š ¬Ã‹Å". Where as when one measure the population mean i.e., the entire variables of a study than the mean is represented by the symbol à ¢Ã¢â€š ¬Ã‹Å" µ, which is pronounced as à ¢Ã¢â€š ¬Ã‹Å"mue and is derived from the Greek letter à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"and can be read as à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"m and can be calculated as . ii. Assume a value from the à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 à ¢Ã¢â€š ¬Ã‹Å"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 give below. Calculate the mean, median and mode of the series. 13. The mean, median and mode of a group of 85 persons were calculated as 28, 31 and 36 respectively. It was later found that while calculating these values, one value was wrongly calculated as 46 instead of the correct value 56. What will be the effect on the correction of this value on the observation? 14. Mr Sachdeva has been heading the computer department of an organization since last 7 years. Following are the year wise expenditure in Rupee for 17 years that has been spent for the maintenance of the computers. 15. Yesh Travels Limited, a travel agent is having 20 cars which are used as taxi in Greater Noida of Uttar Pradesh. The owner of the Travel agent in a surprise check asked the manager the weekly mileage records of all the 20 cars. Being the owner of the travel agent, calculate: (a) the median miles of a car traveled during the week, (b) mean mileage of the cars 16. Delhi Transport Corporation (DTC) is in news since last three months because of repeated cases of fire in its low line buses that is running from different destinations in Delhi city. The high level committee set up of by the chief minister of Delhi is in the process of investigation about the cause of the fire in buses. One of the important causes that the driver of a bus explained is the excessive speed of the buses. It is estimated that in all the routes that the buses are running requires 45 minutes. The sample data derived below shows the arrival time that had taken by some buses to their destination. Conclude from the data the reality. 17. The ages of the students pursuing their master degree in a class is given by following distribution. Estimate the modal value. 18. Calculate the arithmetic mean of the following set of data by using (a) direct method and (b) short-cut method: 19. Following is the daily wage structure of some employees who are working in M/s. Ansul Food Process on daily basis. Calculate the arithmetic mean by using (a) direct method and (b) short-cut method. 20. A candidate has attended three papers like Indian Economics (IE), Statistics (S) and econometrics (E) to clear his M.Phil degree. In each subject he has to appear a oral tests of 40 marks and written test of 60 marks. He secured 25, 21 and 18 marks in oral tests and 52, 35 and 31 marks in written tests in subjects IE, S and E respectively. You have to calculate the weighted average of marks obtained in written test taking the weights percentage of marks obtained in corresponding oral test. 21. A candidate has obtained the following percentage of marks in an examination: Business Law 65, Statistics for Managers 70, Managerial Economics 62, Business Communication 55 and Organisation Behaviour 58. The weights allocated to each subject are as 4, 1, 2, 3, and 3 respectively. Calculate the weighted mean. 22. Tata Motors Limited wanted to offer a cash gift of 7 per cent on the number of cars sold by its sales managers in Northern region of India. Calculate the mode and the median taking the average value. 23. Obtain the median and mode from the following records of a school. 24. Calculate the mean and median of the following data series: 25. Following is the temperature that is maintained in a cold storage in different seasons to preserve the vegetables. Calculate the mean and mode of the series. 26. Find the median from the following data: 27. The distribution of 2000 houses of a locality according to their distance from a petrol pump is given in the following table: 28. A housewife saves Rs. 1/- on the first day, Rs. 2/- on the second day, Rs. 3/- on third day and Rs. 31/- on the 31st day in a particular month. Calculate the mean and median of per day savings. In the amount, her husband contributes Rs. 100 on the 32nd day and Rs. 600/- on the 33rd day. Calculate the new mean and median of savings per day. 29. Compute the mode value of the following data: 30.Calculate the modal value of the following distribution. 31. The distribution of the marks obtained by 70 students of a class in a class is given below: 32. The average rainfall for a week, excluding Sunday, was 12 cms. Sunday was observed heavy rainfall for which when Sunday was included on the other days the average rose to 18 cms. Get how much rainfall was on Sunday? 33. The mean age of the combined group of men and women is 31.5 years. If the mean age of the sub-group of men is 36 years and that of the sub-group of women is 24 years, find out percentage of men and women in the group. 34. The arithmetic mean of 60 items of a series was estimated by an entrepreneur as 22. However, it was latter calculated by the auditor that an item 26 was wrongly calculated as 62. Calculate the correct mean. 35. The sales of a street ice cream seller on seven days of a week during summer season are given below. If the profit is 15% of the sales, find his average profits per day. 36.Calculate the mode of the following data: 37. Calculate the mode of the following distribution: 38. The distribution derived below reveals monthly expenditure on food items incurred by a sample of 135 families in Jalbau Bihar, a residential colony at Greater Noida. Calculate the modal value of the distribution. 39. Calculate the geometric mean of the following data: 40. A distribution is derived below. Calculate the geometric mean. 41. Calculate the geometric mean of the following distribution: 42. In between the years 2005-2009, precious metals changes rapidly in their value in the market. The total rate of return (in %) data is derived in the table below: Calculate the geometric mean of Gold, Diamond and Silver. What conclusions can one draw out of the above result? 43. The data derived below represents the battery life (in minutes) for mobile phones of different brand available in the market. Calculate the mean and median of the series. Calculate the mean deviation, standard deviation.