Choose a useful center

Compare the mean and median, then explain what an unusually large value changes.

Two ways to describe the center

The mean shares the total equally. For 2, 3, 3, 4, 8, the total is 20, so the mean is 20/5 = 4. The dashed line below the axis marks it. Its label, an x with a bar over it, is the usual symbol for a mean.

The median is the middle value after sorting. Here it is 3, labeled M. With an even number of values, there are two middle values, and the median is their mean: for 2, 3, 4, 8 it is (3 + 4)/2 = 3.5. The mean uses every value’s size; the median uses its position. Neither is automatically the best summary.

05101520M = 3x= 42, 3, 3, 4, 8
The same five observations have mean 4 and median 3.

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First lesson in this subject: Read data before calculating

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