Unit 8

Using Box Plots

Lesson 17

Data Sets and Distributions

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Expressions and Equations

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Let's use box plots to make comparisons.

Unit 8 ● Lesson 17

Learning

Goal

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Hours of Slumber

Unit 8 ● Lesson 17 ● Activity 1

Ten sixth-grade students were asked how much sleep, in hours, they usually get on a school night. Here is the five-number summary of their responses.

• Minimum: 5 hours • Median: 7.5 hours • Maximum: 9 hours

• First quartile: 7 hours • Third quartile: 8 hours

1. On the grid, draw a box plot for this five-number summary.

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• What questions could be answered by looking at this box plot?

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Info Gap: Sea Turtles

Unit 8 ● Lesson 17 ● Activity 2

Your teacher will give you either a problem card or a data card. �Do not show or read your card to your partner.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Paper Planes

Unit 8 ● Lesson 17 ● Activity 3

Andre, Lin, and Noah each designed and built a paper airplane. They launched each plane several times and recorded the distance of each flight in yards.

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Work with your group to summarize the data sets with numbers and box plots.

1. Write the five-number summary for the data for each airplane. Then, calculate the interquartile range for each data set.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Paper Planes

Unit 8 ● Lesson 17 ● Activity 3

2. Draw three box plots, one for each paper airplane. Label the box plots clearly.

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• How are the results for Andre and Lin’s planes the same? How are they different?
• How are the results for Lin and Noah’s planes the same? How are they different?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Paper Planes

Unit 8 ● Lesson 17 ● Activity 3

• What can you say about the center of Andre’s data and that of Lin’s data?
• What does the same center tell us in this context?
• What can you say about about the spread of Andre’s data and that of Lin’s data?
• Which of the two planes—Andre’s or Lin’s—flies a more consistent distance? How do you know?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Paper Planes

Unit 8 ● Lesson 17 ● Activity 3

• What do the two very different centers tell us in this context?
• What can you say about the spreads of Lin’s and Noah’s data?
• What does the same range tell us in this case?
• What does the same IQR tell us in this case?
• Whose plane—Lin’s or Noah’s—flies a more consistent distance?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Using Box Plots

Unit 8 ● Lesson 17

• What are some questions you can ask to match box plots to data?
• What does it mean when two box plots show the same median but different IQRs?
• How can we see this in a box plot?
• What does the same median, different IQRs' mean in context?
• What does it mean when two box plots show the same IQR but different medians?
• How can we see this in a box plot?
• What does ‘the same IQR, different medians’ tell us in context?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 8 ● Lesson 17

• I can use a box plot to answer questions about a data set.
• I can use medians and IQRs to compare groups.

Learning Targets

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Humpback Whales

Unit 8 ● Lesson 17 ● Activity 4

Researchers measured the lengths, in feet, of 20 male humpback whales and 20 female humpback whales. Here are two box plots that summarize their data.

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1. How long was the longest whale measured? Was this whale male or female?
2. What was a typical length for the male humpback whales that were measured?
3. Do you agree with each of these statements about the whales that were measured? Explain your reasoning.
1. More than half of male humpback whales measured were longer than 46 feet.
2. The male humpback whales tended to be longer than female humpback whales.
3. The lengths of the male humpback whales tended to vary more than the lengths of the female humpback whales.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

box plot

Unit 8 ● Lesson 17

A box plot is a way to represent data on a number line. The data is divided into four sections. The sides of the box represent the first and third quartiles. A line inside the box represents the median. Lines outside the box connect to the minimum and maximum values.

For example, this box plot shows a data set with a minimum of 2 and a maximum of 15. The median is 6, the first quartile is 5, and the third quartile is 10.

Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

interquartile range (IQR)

Unit 8 ● Lesson 17

The interquartile range is one way to measure how spread out a data set is. We sometimes call this the IQR. To find the interquartile range we subtract the first quartile from the third quartile.

For example, the IQR of this data set is 20 because 50 – 30 = 20.

Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

median

Unit 8 ● Lesson 17

The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.

For the data set 7, 9, 12, 13, 14, the median is 12.

For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. 6 + 8 = 14 and 14 ÷ 2 = 7.

Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

quartile

Unit 8 ● Lesson 17

Quartiles are the numbers that divide a data set into four sections that each have the same number of values.

For example, in this data set the first quartile is 30. The second quartile is the same thing as the median, which is 43. The third quartile is 50.

Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

range

Unit 8 ● Lesson 17

The range is the distance between the smallest and largest values in a data set.

For example, for the data set 3, 5, 6, 8, 11, 12, the range is 9, because 12 – 3 = 9.

Glossary

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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