# 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 100^{th} percentile. From this same perspective, the median, which has 50% of the observations at or below it, is the 50^{th} percentile. The *p ^{th}* 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 25^{th} percentile and the 75^{th} percentile. The 25^{th} percentile demarcates the **first quartile**, the median or 50^{th} percentile demarcates the second **quartile**, the 75^{th} percentile demarcates the **third quartile**, and the 100^{th} percentile demarcates the **fourth quartile**.

The **interquartile range** represents the central portion of the distribution, and is calculated as t**he 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

25^{th} percentile = 4; 75^{th} percentile = 16;

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

# Have I Grasped the Key Concepts Here?