variation (statistical)

variation (statistical) The greater part of empirical research is concerned with the characteristics of groups, or aggregate social entities, rather than individual cases; that is, with men or women in general, rather than any particular man or woman. A range of statistical measures of association are employed to describe the features of groups, or types of case in the aggregate. Most of them are based on the normal distribution, the Binomial distribution, or the Poisson distribution, from which a number of statistical summary measures are derived. The mean, mode, and median provide measures of central tendency, the most common or typical value in the distribution, which coincide when the distribution is normal. Measures of dispersion attempt to concentrate information about the general pattern in single summary statistics. These include the range, mean deviation, quartile deviation, decile range, and the standard deviation, which is by far the most important. One of the properties of the normal distribution is that about 68 per cent of all cases are contained within one standard deviation on either side of the mean, about 95 per cent lie within two standard deviations, and some 99.73 per cent lie within three standard deviations on either side of the mean. The standard deviation of a distribution thus summarizes a great deal of information about the overall dispersion, the degree of clustering or concentration around the mean. The variance is the square of the standard deviation, and has the property of being additive. Analysis of variance measures variance within sub-groups in the data-set, and between the averages of these sub-groups. See also MEASUREMENT; SAMPLING.