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11.8: Box-and-Whisker Plots

Difficulty Level: At Grade Created by: CK-12
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Learning Objectives

At the end of this lesson, students will be able to:

  • Make and interpret box-and-whisker plots.
  • Analyze effects of outliers.
  • Make box-and-whisker plots using a graphing calculator.


Terms introduced in this lesson:

first quartile, third quartile
five number summary
inter-quartile range (IQR)
raw data
ordered list
outlier, mild outlier, extreme outlier

Teaching Strategies and Tips

Use the introduction to point out that the median can be used to divide a data set into four quarters. See also Examples 1 and 2.

  • After finding the quartiles, it is possible to construct the five-number summary and corresponding box-and-whisker plot.
  • After finding the quartiles, it is possible to calculate the IQR.

Emphasize interpreting the box plot:

  • \begin{align*}50 \%\end{align*} of the data set lies between the first and third quartiles (IQR).
  • \begin{align*}75 \%\end{align*} of the data set lies above the first quartile; \begin{align*}75 \%\end{align*} of the data set lies below the third quartile.
  • The range is the distance from one whisker to the other.
  • Compare the relative size of the box to the length of the whiskers: short whiskers indicate clustered data; long whiskers indicate a spread-out data set.
  • If one whisker is shorter than another, then the distribution is skewed.

Construct box-and-whisker plots for two data sets and compare them side-by-side. Point out that this makes drawing inferences easy. See Example 3.

Compare the range and IQR for a data set. Ask:

  • For what kind of distributions should the IQR be used? the range?

Additional Example:

For the data set below, calculate the range and IQR. Which measure of dispersion do you think will give a better indication of the spread in the data?

\begin{align*}2, 5, 8, 8, 8, 9, 9, 10, 100\end{align*}

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