Range

Let A={2, 6, 10, 14, 18} and B={5, 7, 10, 13, 15}.

For A, the mean is (2+6+10+14+18)/5 = 50/5 = 10, the median is 10 and the midrange is 10.

For B, the mean is (5+7+10+13+15)/5 = 50/5 = 10, the median is 10 and the midrange is 10.

While these sets have the same measures of central tendency, they are not identical sets of numbers. One way in which they differ is that they have different largest and smallest values.

Definition . The range of a set of data values is the difference between the largest value and the smallest value.

For data set A the range is 18 - 2 = 16.

For data set B the range is 15 - 5 = 10.

Example

Below are the sorted weights of 50 high school students. Find the range.

Solution .

Since the smallest value is 82 and the largest is 230, the range is 230 - 82 = 148.