Central tendency

For each group, the mean income is higher than the median, indicating a positively skewed distribution where there are few extremely high values. When looking at individual groups, the largest difference between mean and median is within the white workers group; there is nearly a $21,000 ($20,651) difference, well above the other two groups as well as all workers.  Black workers see a difference of $15,026 between mean and median income and the difference among Latino workers is $16,700. I think white workers have the greatest absolute difference between mean and median because more white workers than black and Latino workers occupy high paying jobs, thus creating the largest difference among white workers.

In this case the mean is pulled in the direction of the extreme high incomes, creating an inflated mean income level. When interval-ratio variables are skewed such as this, it is best to choose either mode or median as the measure of central tendency.  For this reason, I would choose median as that is the measure of central tendency that represents the exact middle, alleviating the skewed effect of the extreme values on the high end.

 

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Examine figure below from the chapter’s “A Closer Look 4.2, A Cautionary Note: Representing Income.” Overall, how would you describe the differences between the median and mean incomes for each group? Why do you think white workers have the greatest absolute difference between median and mean incomes? If you had to report only one of these measures of central tendency, which one would you choose and why?