How to Find the Interquartile Range (IQR) of a Box Plot


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.

Interquartile range of a box plot

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

Box Plot Generator
How to Compare Box Plots
How to Identify Skewness in Box Plots
How to Interpret the Interquartile Range

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