Measures of Variability

Liam M. O'Brien

Numerical summaries used to describe a set of data generally include a measure of central tendency. While this provides a single estimate that describes where the data are located, it does not describe how spread out the data are about this central point. There are several numerical summaries that describe the variability in a data set. Four of the most common are the variance, the standard deviation, the interquartile range (IQR), and the range. They are illustrated in Table 1 using data collected on height from 22 subjects. The variance is approximately equal to the average squared distance of each observation about the mean and is generally denoted by s 2 . This is most easily seen in its formula, which is given by where x i represents the individual observation from the ith subject; the mean of the data is given by x; σ is the summation sign, which ...

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