# 11.8: Box-and-Whisker Plots

**At Grade**Created by: CK-12

## 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.

## Vocabulary

Terms introduced in this lesson:

- first quartile, third quartile
- five number summary
- whiskers
- inter-quartile range (IQR)
- range

- 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*}

## Error Troubleshooting

NONE.