A Measure of Variation: Range
Consider these three sets of quiz scores:
Section A: 5 5 5 5 5 5 5 5 5 5
Section B: 0 0 0 0 0 10 10 10 10 10
Section C: 4 4 4 5 5 5 5 6 6 6
All three of these sets of data have a mean of 5 and median of 5, yet the sets of scores are clearly quite different. In section A, everyone had the same score; in section B half the class got no points and the other half got a perfect score, assuming this was a 10-point quiz. Section C was not as consistent as section A, but not as widely varied as section B.
In addition to the mean and median, which are measures of the “typical” or “middle” value, we also need a measure of how “spread out” or varied each data set is.
There are several ways to measure this “spread” of the data. In this section, we focus on the simplest of these measures called the range.
Range
The range is the difference between the maximum value and the minimum value of the data set.
example
Using the quiz scores from the previous example (shown in the table below), find the range for each section.
| Section A: | 5 5 5 5 5 5 5 5 5 5 |
| Section B: | 0 0 0 0 0 10 10 10 10 10 |
| Section C: | 4 4 4 5 5 5 5 6 6 6 |
In this example, the range seems to be revealing how spread out the data is. However, suppose we add a fourth section, Section D, with scores 0 5 5 5 5 5 5 5 5 10.
This section also has a mean and median of 5. The range is 10, yet this data set is quite different than Section B. To better illuminate the differences, we’ll have to turn to more sophisticated measures of variation.
This example is explained in the following video.
