*30*

A **box plot** is a type of plot that displays the five number summary of a dataset, which includes:

- The minimum value
- The first quartile (the 25th percentile)
- The median value
- The third quartile (the 75th percentile)
- The maximum value

To make a box plot, we draw a box from the first to the third quartile. Then we draw a vertical line at the median. Lastly, we draw “whiskers” from the quartiles to the minimum and maximum value.

The **interquartile range**, often abbreviated IQR, is the difference between the third quartile and the first quartile.

- IQR = Q3 – Q1

This tells us how spread out the middle 50% of values are in a given dataset.

The following examples show how to find the interquartile range (IQR) of a box plot in practice.

**Example 1: Exam Scores**

The following box plot shows the distribution of scores on a certain college exam. What is the interquartile range of the exam scores?

We can find the following values on the box plot to answer this:

- Q3 (Upper Quartile) = 90
- Q1 (Lower Quartile) = 70
- Interquartile Range (IQR) = 90 – 70 = 20

The interquartile range of the exam scores is **20**.

**Example 2: Points Scored**

The following box plot shows the distribution of points scored by basketball players in a certain league. What is the interquartile range of the distribution?

We can find the following values on the box plot to answer this:

- Q3 (Upper Quartile) = 27
- Q1 (Lower Quartile) = 15
- Interquartile Range (IQR) = 27 – 15 = 12

The interquartile range of the distribution is **12**.

**Example 3: Comparing Plant Heights**

The following box plots show the distribution of heights for two different plant species: Red and Blue. Which distribution has a larger interquartile range?

First, let’s find the interquartile range of the red box plot:

- Q3 (Upper Quartile) = 30
- Q1 (Lower Quartile) = 20
- Interquartile Range (IQR) = 30 – 20 =
**10**

Next, let’s find the interquartile range of the blue box plot:

- Q3 (Upper Quartile) = 27
- Q1 (Lower Quartile) = 15
- Interquartile Range (IQR) = 27 – 15 =
**12**

The interquartile range for the Blue species is larger.

**Additional Resources**

The following tutorials provide additional information about box plots:

Box Plot Generator

How to Compare Box Plots

How to Identify Skewness in Box Plots

How to Interpret the Interquartile Range