The Empirical Rule: Working the Standard Deviation
The values of many large data sets tend to cluster around the mean or median so that the data distribution in the histogram resembles a bell-shape, symmetrical curve. When this is the case, the empirical rule (sounds like a decree from the emperor) tells us that approximately 68 percent of the data values will be within one standard deviation from the mean.
According to the empirical rule, if a distribution follows a bell-shape—a symmetrical curve centered around the mean—we would expect approximately 68, 95, and 99.7 percent of the values to fall within one, two, and three standard deviations around the mean respectively.
For example, suppose that the average exam score ...