How can we use descriptive statistics to characterize our data? When I was teaching at the University of Tennessee I found a curious statement in a textbook that offered a practical answer to this question. This statement was labeled as “the Empirical Rule,” and it is the subject of what follows.

The empirical rule

While a statistic may provide a mathematical summary for the data, it has to be understandable before it can truly be said to be descriptive. While the average is easy to understand, most students have trouble understanding the standard deviation statistic. The empirical rule converts the average and standard deviation statistics into comprehensible statements about the data using three intervals centered on the average. The first interval has a radius equal to the standard deviation statistic, the second has a radius equal to twice the standard deviation statistic, and the third has a radius equal to three times the standard deviation statistic.

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