9.3 Describing Dispersion

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• Math Help

The histograms in Example 4 have normal distributions drawn on them because they can be approximated by normal distributions. This can be shown by comparing the percents found using the normal distribution and the actual data for several heights. Use 61 inches and 67 inches. A height of 61 inches is 3 standard deviations below the mean for males and about 1 standard deviation below the mean for females (notice that for females, 61.5 inches is exactly 1 standard deviation below the mean). A height of 67 inches is 1 standard deviation below the mean for males and about 1 standard deviation above the mean for females (notice that for females, 66.5 inches is exactly 1 standard deviation above the mean).

At most 61 inches tall

At least 67 inches tall

You can see from these tables that the percents using the normal distribution are close to the percents using the actual data for males and females.

• Consumer Suggestion

Women have historically received less pay for equal work in the United States. As a current average, women earn 77% the amount of their male counterparts. To see what the gender salary gap is like in your state, the American Association of University Women (AAUW) has compiled state-by-state data into this table.

• Checkpoint Solution

While Judge and Cable's study indicates a positive correlation between height and salary, this does not guarantee that a taller person will always be more successful than a shorter person. Many things matter for career success such as experience, who you know, personality, and intelligence. Each of these traits is weighted differently for different types of careers. It is not so much a question of whether height matters but a question of how much height matters. If you are a basketball player, height certainly matters for career success. If you run an online business from home, height probably does not matter at all.

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