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# 11.8: Box-and-Whisker Plots

Difficulty Level: 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:

• 50%\begin{align*}50 \%\end{align*} of the data set lies between the first and third quartiles (IQR).
• 75%\begin{align*}75 \%\end{align*} of the data set lies above the first quartile; 75%\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?

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?

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

## Error Troubleshooting

NONE.

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