Measures of Dispersion

Abstract

In the last chapter, we covered how to use R functions to calculate various measures of central tendency. But while it is certainly useful to know the mean of a given variable you are examining, it is even more helpful if you also know the spread, or dispersion, of cases around this mean. For this chapter, we will focus on measures of dispersion for both nominal-/ordinal-level variables (variation ratio and index of qualitative variation) and ratio-/interval-level variables (range, variance, standard deviation, and coefficient of relative variation). We will use data from the 2004 Survey of Inmates in State and Federal Correctional Facilities, a nationally representative sample of US prison inmates to demonstrate some of these concepts.

Key Terms

Coefficient of variation (CV)

A measure of dispersion calculated by dividing the standard deviation by the mean.

Index of qualitative variation (IQV)

A measure of dispersion calculated by dividing the sum of the possible pairs of observed scores by the sum of the possible pairs of expected scores (when cases are equally distributed across categories).

Range

A measure of dispersion calculated by subtracting the smallest score from the largest score. The range may also be calculated from specific points in a distribution, such as the 5th and 95th percentile scores.

Standard deviation (SD)

A measure of dispersion calculated by taking the square root of the variance.

Variance (s²)

A measure of dispersion calculated by adding together the squared deviation of each score from the mean and then dividing the sum by the number of cases.

Variation ratio (VR)

A measure of dispersion calculated by subtracting the proportion of cases in the modal category from 1.