measures of central tendency
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measures of central tendencythe different ways of conceptualizing the central or middle position of a group of observations, numbers, etc. There are three measures of central tendency: the mode, the median and the mean. The mode is the value which occurs most often. The median is the value which occupies the central position, having as many values below as above it. The mean (more commonly called the average) is found by adding together each individual value and dividing by the number of cases, or observations.
Sometimes a set of observations will yield a bimodal distribution (where two different values occur most often). Also, if there is an even number of observations there is no central value to represent the median. In this case the median may be taken to lie midway between the two centrally placed values.
Where there are many values in the distribution the approximate value of the median can be calculated by interpolation. The data is first grouped into a set number of bands and the median is taken as lying within the middle group, its value being calculated mathematically by estimating its position from the percentage of cases lying in the lower and higher bands.
The choice of which measure of central tendency to employ is determined by two factors: the level of measurement (see CRITERIA AND LEVELS OF MEASUREMENT) being employed and the amount of dispersion in the set of observations. Where a nominal-level measure is being employed, only the mode should be calculated. For example, if numerical values have been assigned to different types of accommodation, then the mode will show which is the most popular type of accommodation, but both the mean and the median would be meaningless. The median is best used with ordinal-level measures where the relative distances between categories is unknown (although it should be said that many social scientists do use the mean when dealing with ordinal-level variables because of the large number of statistical tests which can then be undertaken). Finally, the mean is generally the best statistic to use with interval level measures, except in those instances in which there are a number of extreme values which skew the distribution. For example, the mean incomes of a group of respondents may be skewed because of the inclusion in the sample of a few high-income earners. In such instances the median is often a better statistic to employ. Another instance where the median might be calculated is where data has been grouped and the ‘highest’ category is open-ended. For example, income might have been grouped in such a way that all earning over £100,000 per annum are grouped together and there is no upper limit to the amount which people in the category earn. In such a case the mean cannot be calculated, but the value of the median can be estimated by the process of interpolation mentioned above. see also MEASURES OF DISPERSION.