Percentiles, Quartiles, and Interquartile Range

We can consider the maximum value of a distribution in another way. We can think of it as the value in a set of data that has 100% of the observations at or below it. When we consider it in this way, we call it the 100th percentile. From this same perspective, the median, which has 50% of the observations at or below it, is the 50th percentile. The pth percentile of a distribution is the value such that p percent of the observations fall at or below it.

The most commonly used percentiles other than the median are the 25th percentile and the 75th percentile. The 25th percentile demarcates the first quartile, the median or 50th percentile demarcates the second quartile, the 75th percentile demarcates the third quartile, and the 100th percentile demarcates the fourth quartile.

The interquartile range represents the central portion of the distribution, and is calculated as the difference between the third quartile and the first quartile. This range includes about one-half of the observations in the set, leaving one-quarter of the observations on each side as shown in Figure 3.8 below.

Now let's look at an example on how to calculate interquartile range, suppose in a distribution, we find

25th percentile = 4; 75th percentile = 16;

Then interquartile range = 75th percentile - 25th percentile = 16 - 4 = 12