EXAMPLE 6 Mean versus median

Table 12.1 gives the approximate salaries (in millions of dollars) of the 15 members of the Cleveland Cavaliers basketball team for the 2014–2015 season. You can calculate that the mean is million and that the median is million. No wonder professional basketball players have big houses.

Why is the mean so much higher than the median? Figure 12.8 is a stemplot of the salaries, with millions as stems. The distribution is skewed to the right, and there are two high outliers. The very high salaries of LeBron James and Kevin Love pull up the sum of the salaries and so pull up the mean. If we drop the outliers, the mean for the other 13 players is only $3.5 million. The median doesn’t change nearly as much: it drops from $2.7 million to $2.6 million.

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We can make the mean as large as we like by just increasing LeBron James's salary. The mean will follow one outlier up and up. But to the median, LeBron’s salary just counts as one observation at the upper end of the distribution. Moving it from $20.6 million to $206 million would not change the median at all.