# 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:

- of the data set lies between the first and third quartiles (IQR).
- of the data set lies above the first quartile; 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?*

## Error Troubleshooting

NONE.

### Image Attributions

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CK.MAT.ENG.TE.1.Algebra-I.11
Common Misconceptions
Concept Check and Troubleshooting
Differentiated Instruction
dispersion
distance formula
Enrichment
extraneous solutions
histograms
hypotenuse
Inquiry Process
mean
Measures of Central Tendency
median
midpoint formula
mode
outliers
Pacing
Problem Sets
Problem Solving
Pythagorean theorem
Quizzes
radical equations
radical expressions
radical sign
range
rationalizing the denominator
Science Inquiry
simple harmonic motion
Solution Key
Solutions
square root functions
standard deviation
stem-and-leaf plots
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
variance
Worksheets

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Solutions
Solution Key
Answers
(43 more)
Problem Sets
Tests
Teacher Edition
Quizzes
Assessment
Inquiry Process
Testing
Problem Solving
Concept Check and Troubleshooting
Enrichment
Teaching Strategies
Differentiated Instruction
Pythagorean theorem
histograms
box-and-whisker plots
stem-and-leaf plots
range
mode
median
mean
Measures of Central Tendency
dispersion
radical equations
radical expressions
square root functions
outliers
standard deviation
variance
midpoint formula
distance formula
hypotenuse
extraneous solutions
radical sign
rationalizing the denominator
simple harmonic motion
Pacing
Common Misconceptions
Science Inquiry
Teaching Strategies and Tips
Activities
Worksheets
CK.MAT.ENG.TE.1.Algebra-I.11

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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