4 - Measures of Variability

Abstract

This chapter provides an overview of measures of variability. Any distribution can be concisely described by assigning it a measure of central tendency and a measure of variability. There are three commonly used measures of variability: the range, the standard deviation, and the interquartile range. The range is the easiest measure of variability to calculate. The range is the crudest and least informative measure of dispersion. The standard deviation is the measure of variability that corresponds to the mean as a measure of central tendency. The standard deviation is the square root of the average squared deviation from the mean. It is calculated in four stages: (1) the deviation of each item in the distribution from the mean is noted, (2) each of these deviation scores is squared, (3) the mean of these squared deviations is calculated, and (4) the square root of this mean is then calculated; this is the standard deviation of the distribution. The mean squared deviation, the penultimate stage in working out the standard deviation, is called the variance of the distribution.