Example 12.3

EXAMPLE 3 Income inequality

To investigate income inequality, we compare household incomes of Hispanics, blacks, and whites. The Census Bureau website provides information on income distribution by race. Figure 12.3 compares the income distributions for Hispanics, blacks, and whites in 2013. This figure is a variation on the boxplot idea. The largest income among several million people will surely be very large. Figure 12.3 uses the 95% points (the values representing where the top 5% of incomes start) in the distributions instead of the single largest incomes. So, for example, the line above the box for the Hispanic group extends only to $144,040 rather than to the highest income. Many statistical software packages allow you to produce boxplots that suppress extreme values, but the rules for what constitutes an extreme value usually do not use the 95% point in the distribution instead of the single largest value.

Figure 12.3: Figure 12.3 Boxplots comparing the distributions of income among Hispanics, blacks, and whites. The ends of each plot are at 0 and at the 95% point in the distribution.

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Figure 12.3 gives us a clear and simple visual comparison. We see that the median and middle half are slightly greater for Hispanics than for blacks and that for whites the median and middle half are greater than for both blacks and Hispanics. The income of the bottom 5% stays small because there are some people in each group with no income or even negative income, perhaps due to illness or disability. The 95% point, marking off the top 5% of incomes, is greater for whites than for either blacks or Hispanics, and the 95% point of incomes for Hispanics is greater than for blacks. Overall, incomes for whites tend to be larger than those for Hispanics and blacks, highlighting racial inequities in income.

Figure 12.3 also illustrates how boxplots often indicate the symmetry or skewness of a distribution. In a symmetric distribution, the first and third quartiles are equally distant from the median. In most distributions that are skewed to the right, on the other hand, the third quartile will be farther above the median than the first quartile is below it. The extremes behave the same way. Even with the top 5% not present, we can see the right-skewness of incomes for all three races.