Empirical Rule Demonstration (5)

Having calculated both the mean and the standard deviation, we can now calculate the intervals into which we would expect the various percentages to fall. Because we are working with whole numbers, these intervals will have to be rounded quite a lot, which may lead to a loss of accuracy, particularly with part 1 of the rule, which is the weakest part.

The table below shows the three parts of the empirical rule. The minimum and maximum column values for the first part of the rule have been entered into the table already. They were calculated from the mean (15.32) and standard deviation (1.38) which you have just calculated. Complete the table for yourself, using these values. Remember to round your answers to the nearest whole number. When you are ready, click the button to check your answers.

Rule Min. Column Max. Column
60%-75% within ±1 standard deviation of the mean 14 17
90%-98% within ±2 standard deviations of the mean
99%-100% within ±3 standard deviations of the mean