# Social Statistics for a Diverse Society

# Chapter Summary

**Chapter 5**

Measures of variability are numbers that describe how much variation or diversity there is in a distribution.

The index of qualitative variation (IQV) is used to measure variation in nominal variables. It is based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution. IQV can vary from 0.00 to 1.00.

The range measures variation in interval-ratio variables and is the difference between the highest (maximum) and the lowest (minimum) scores in the distribution. To find the range, subtract the lowest from the highest score in a distribution. For an ordinal variable, just report the lowest and the highest values without subtracting.

The interquartile range (IQR) measures the width of the middle 50% of the distribution. It is defined as the difference between the lower and upper quartiles (*Q*1 and *Q*3). For an ordinal variable, just report *Q*1 and *Q*3 without subtracting.

The box plot is a graphical device that visually presents the range, the IQR, the median, the lowest (minimum) score, and the highest (maximum) score. The box plot provides us with a way to visually examine the center, the variation, and the shape of a distribution.

The variance and the standard deviation are two closely related measures of variation for interval-ratio variables that increase or decrease based on how closely the scores cluster around the mean. The variance is the average of the squared deviations from the center (mean) of the distribution; the standard deviation is the square root of the variance.