central tendency (measures of)

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central tendency (measures of) A statistical term applied to the central value in a frequency distribution—commonly referred to as the average. Depending on the level of measurement of the variable (nominal, ordinal, interval, or ratio), and the shape of the distribution (normal or otherwise), various measures of central tendency may be calculated. The mean is the most well-known, and is obtained by adding together all the individual values in a set of measurements, then dividing the sum by the total number of cases in the set—to give the average age, height, temperature, or whatever. However, if a particular distribution is highly skewed (that is, if there are several numbers of extreme value at one or other end of the series), then it may make more sense to calculate the median. The median is literally the middle value in a series of numbers, and may be used in place of the mean when, for example, average income is calculated, since the distribution of income is generally highly skewed. The third measure of central tendency, the mode, is used to describe the most frequently occurring category of a non-numeric variable (for example voting intention). It is less frequently employed than the mean or median.

Any elementary statistical textbook will supply formulae for the calculation of measures of central tendency. The following examples may help to illustrate the principles outlined above. If, for example, a poll of voters in a small town suggests that 40 per cent will vote Republican, 35 per cent will vote Democrat, while 25 per cent will not vote at all, then we may say that the typical voter among these townspeople is a Republican. This is the category which has the largest representation—the mode. (A distribution with two modal categories is termed bimodal.) By comparison, the median value in a series is the middle case; or, more precisely, the point which neither exceeds nor is exceeded by more than 50 per cent of the total observations. For example, a number of students might be tested in an examination and receive the following grades: Joan—B, Bill—C, James—D, Brett—F, Joyce—F. In this distribution, the middle case is James, since he has two students ranking above and two below him. The median mark is therefore D. The mean is the measurement of central tendency most people have in mind when they talk about ‘the average’. For example, we may record the number of times a particular university professor at his or her desk is interrupted by telephone calls each day for a week, and obtain the following data: Monday = 4, Tuesday = 6, Wednesday = 4, Thursday = 4, Friday = 2, Saturday = 4. The average number of interruptions per day is therefore 24 (total number of scores in the set) divided by 6 (the number of cases)—giving a mean of 4 calls each day. See also SKEWNESS.