Reading a Distribution and Its Skew

Reading a distribution means asking how values spread around the average, because a mean describes a symmetric spread well and a skewed one badly.

A department reports mean graduate earnings of $95,000. The figure is arithmetically correct and describes almost nobody. Ninety-eight graduates earn about $45,000; two earn several million, and those two drag the mean upward. The median — the middle value, half above and half below — is $45,000, and it is the honest summary. The procedure: ask for the median alongside the mean, and treat a large gap between them as the signal. Mean far above median means a long tail of high values; mean far below means a tail of low ones. Then ask for the range or the quartiles, because two distributions with identical medians can describe entirely different situations. Income, wealth, and housing cost are skewed almost everywhere, so for those variables the mean is the number to distrust first.