SAT One-Variable Data study notes

Mean, median, and range answer different questions. The mean uses every value; the median is the middle after sorting; range is maximum minus minimum. A single extreme value can move the mean a lot while barely changing the median.

Worked example

Five delivery times are 18, 21, 22, 24, and 35 minutes. The 35-minute delivery is replaced with a 25-minute delivery. How do the mean, median, and range change?

The original total is 120, so the mean is 24. The median is 22 and the range is 35 - 18 = 17. Replacing 35 with 25 lowers the total to 110, giving a mean of 22. In the sorted new list, 18, 21, 22, 24, 25, the median remains 22 and the range is 25 - 18 = 7. The mean and range change; the median does not.

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