How to Calculate the Range

Finds the largest and smallest values of a data set and the range, their difference. The range is the simplest measure of spread.

Explanation

The range is the difference between the largest and the smallest value in a data set — the simplest measure of spread there is.

R = x_{\max} - x_{\min}

Example

For the data 12, 15, 18, 20, 25 the maximum is 25 and the minimum is 12.

R = 25 - 12 = 13

Watch out

The range is easy to grasp, but it is a blunt instrument.

It uses only two values. Everything between the extremes could be arranged any way at all and the range would not change
It is extremely sensitive to outliers. One freak value inflates it on its own
It tends to grow with the number of observations, so comparing the ranges of samples of different sizes is unfair

For a serious look at spread, use the standard deviation, which uses every value, or the interquartile range, which resists outliers. The range is for a quick sense of the overall width.