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• LESSON PLAN 7-5

Box-and-Whisker Plots Objective: To display and analyze data in box-and- whisker plots Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY

Data Analysis and Statistics/ Probability Benchmark:

E-2.6: I can display and analyze data in box-and-whisker plots and circle graphs

Introduction & Development: Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters. A box-and-whisker plot uses a number line to show the distribution of a set of data. To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile, divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile. Example One: Making a Box-and-Whisker Plot Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.

Learn to display andanalyze data in box-and-whisker plots.

Vocabulary

interquartile range

upper quartile

lower quartile

box-and-whisker plot

Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters.

A uses a number line to show the distribution of a set of data.

To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile,divides the data into a lower half and an upper half. The median of the lower half is the , and the median of the upper half is the .

Making a Box-and-Whisker Plot

Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upperquartiles.

Step 2: Draw a number line. Above the number line, plot a point foreach value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside thebox, draw a vertical line through the median. Then draw thewhiskers from the box to the least and greatest values.

upper quartilelower quartile

box-and-whisker plot

15 20 25 3010

17LeastvalueGreatest

value

Lower quartileMedian

Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282

394 Chapter 7 Collecting, Displaying, and Analyzing Data

7-5 Box-and-Whisker Plots

15 20 25 3010

E X A M P L E 1

To find the median of a data set with aneven number ofvalues, find the meanof the two middlevalues.

• Step 2: Draw a number line. Above the number line, plot a point for each value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median. Then draw the whiskers from the box to the least and greatest values.

The interquartile range of a data set is the difference between the lower and upper quartiles. It tells how large the spread of data around the median is. You can use a box-and-whisker plot to analyze how data in a set are distributed. You can also use box-and-whisker plots to help you compare two sets of data. Example Two: Comparing Box-and-Whisker Plots The box-and-whisker plots below show the distribution of the number of fish caught per trip by two fishing charters.

Which fishing charter has a greater median?

The median number of fish caught on Reel-to-Reel Charters, about 54, is greater

Learn to display andanalyze data in box-and-whisker plots.

Vocabulary

interquartile range

upper quartile

lower quartile

box-and-whisker plot

Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters.

A uses a number line to show the distribution of a set of data.

To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile,divides the data into a lower half and an upper half. The median of the lower half is the , and the median of the upper half is the .

Making a Box-and-Whisker Plot

Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upperquartiles.

Step 2: Draw a number line. Above the number line, plot a point foreach value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside thebox, draw a vertical line through the median. Then draw thewhiskers from the box to the least and greatest values.

upper quartilelower quartile

box-and-whisker plot

15 20 25 3010

17LeastvalueGreatest

value

Lower quartileMedian

Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282

394 Chapter 7 Collecting, Displaying, and Analyzing Data

7-5 Box-and-Whisker Plots

15 20 25 3010

E X A M P L E 1

To find the median of a data set with aneven number ofvalues, find the meanof the two middlevalues.

Learn to display andanalyze data in box-and-whisker plots.

Vocabulary

interquartile range

upper quartile

lower quartile

box-and-whisker plot

Carson is planning a deep-sea fishing trip. He chooses a fishing charter based on the number of fish caught on different charters.

A uses a number line to show the distribution of a set of data.

To make a box-and-whisker plot, first divide the data into four parts using quartiles. The median, or middle quartile,divides the data into a lower half and an upper half. The median of the lower half is the , and the median of the upper half is the .

Making a Box-and-Whisker Plot

Use the data to make a box-and-whisker plot.

26, 17, 21, 23, 19, 28, 17, 20, 29

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upperquartiles.

Step 2: Draw a number line. Above the number line, plot a point foreach value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside thebox, draw a vertical line through the median. Then draw thewhiskers from the box to the least and greatest values.

upper quartilelower quartile

box-and-whisker plot

15 20 25 3010

17LeastvalueGreatest

value

Lower quartileMedian

Upper quartile

17 19 20 21 23 26 28 29

= 1817 + 192

= 2726 + 282

394 Chapter 7 Collecting, Displaying, and Analyzing Data

7-5 Box-and-Whisker Plots

15 20 25 3010

E X A M P L E 1

To find the median of a data set with aneven number ofvalues, find the meanof the two middlevalues.

The of a data set is the difference between thelower and upper quartiles. It tells how large the spread of data aroundthe median is.

You can use a box-and-whisker plot to analyze how data in a set aredistributed. You can also use box-and-whisker plots to help you comparetwo sets of data.

Comparing Box-and-Whisker Plots

The box-and-whisker plots below show the distribution of thenumber of fish caught per trip by two fishing charters.

Which fishing charter has a greater median?The median number of fish caught on Reel-to-Reel Charters,about 54, is greater than the median number of fish caughton Mud Puppy Charters, about 51.

Which fishing charter has a greater interquartile range?The length of the box in a box-and-whisker plot indicates theinterquartile range. Reel-to-Reel Charters has a longer box, soit has a greater interquartile range.

Which fishing charter appears to be more predictable in thenumber of fish that might be caught on a fishing trip?The range and interquartile range are smaller for Mud PuppyCharters, which means that there is less variation in the data.So the number of fish caught on Mud Puppy Charters is morepredictable.

interquartile range

Think and Discuss

1. Describe what you can tell about a data set from abox-and-whisker plot.

2. Explain how the range and the interquartile range ofa set of data are different. Which measure tells you moreabout central tendency?

2E X A M P L E

20 30 40 50 60 70 80

= Reel-to-Reel Charters

= Mud Puppy Charters

Number of fish

7-5 Box-and-Whisker Plots 395

• than the median number of fish caught on Mud Puppy Charters, about 51. Which fishing charter has a greater interquartile range?

The length of the box in a box-and-whisker plot indicates the interquartile range. Reel-to-Reel Charters has a longer box, so it has a greater interquartile range.

Which fishing charter appears to be more predictable in the number of fish that might be caught on a fishing trip?

The range and interquartile range are smaller for Mud Puppy Charters, which means that there is less variation in the data. So the number of fish caught on Mud Puppy Charters is more predictable.

Complete Lesson 7-5 Practice A with the class for additional instruction Assessment:

Students participation in examples Completion of Practice B & C

• LESSON PLAN 7-6

Line Graphs Objective: To display and analyze data in line graphs Grade Level: 6th Grade Estimated Time: 90 minutes Mathematics Academic Standards: STANDARD E: STATISTICS AND PROBABILITY

Data Analysis and Statistics/ Probability Benchmark:

E-2.6: I can display and analyze data in bar and line graphs Introduction