THE RANGE OF THE MIDDLE 50% OF THE VALUES

September 24, 2025

The range is the simplest measure of spread. It is the difference between the highest and the lowest values in the observations.

A variable's range needs to be examined carefully. Range inspection is a good practical method to find the presence of errors in observations (a data set). Sometimes, an unusually wide range is caused by an extreme value. Extreme values are also called outliers.

The interquartile range—the difference between the 75^th and 25^th percentile values (50% of the values in the middle)—may be a better measure of spread.

Let's calculate the interquartile range

• Example (i): A data set with 9 observations (8, 13, 11, 13, 19, 16, 15, 21, 25)
• Example (ii): A data set with 12 observations (4, 9, 5, 9, 9, 13, 11, 11, 15, 15, 17, 18)
• (i) Order the data: 8, 11, 13, 13, 15, 16, 19, 21, 25
• (ii) Order the data: 4, 5, 9, 9, 9, 11, 11, 13, 15, 15, 17, 18

• Example iii: A data set with 5 observations ( 65, 72, 68, 80, 165). The data set’s minimum value is 65 and its maximum value is 165. The range is 100. However, most of the values are within a range of 15. The interquartile range is 12. The extreme value does not affect the interquartile range. The interquartile range represents most of the values in the observations better.