Unit 8

Using Histograms to Answer Statistical Questions

Lesson 7

Data Sets and Distributions

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Expressions and Equations

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Let's draw histograms and use them to answer questions.

Unit 8 ● Lesson 7

Learning

Goal

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Questions

Unit 8 ● Lesson 7 ● Activity 1

Here are four questions about the population of Alaska. Which question does not belong? Be prepared to explain your reasoning.

1. In general, at what age do Alaska residents retire?
2. At what age can Alaskans vote?
3. What is the age difference between the youngest and oldest Alaska residents with a full-time job?
4. Which age group is the largest part of the population: 18 years or younger, 19–25 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, or 65 years or older?

Warm-up: Which One Doesn’t Belong?

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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.

Measuring Earthworms

Unit 8 ● Lesson 7 ● Activity 2

An earthworm farmer set up several containers of a certain species of earthworms so that he could learn about their lengths. The lengths of the earthworms provide information about their ages. The farmer measured the lengths of 25 earthworms in one of the containers. Each length was measured in millimeters.

1. Using a ruler, draw a line segment for each length:
1. 20 millimeters
2. 40 millimeters
3. 60 millimeters
4. 80 millimeters
5. 100 millimeters

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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.

Measuring Earthworms

Unit 8 ● Lesson 7 ● Activity 2

2. Here are the lengths, in millimeters, of the 25 earthworms.

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Complete the table for the lengths of the 25 earthworms.

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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.

Measuring Earthworms

Unit 8 ● Lesson 7 ● Activity 2

3. Use the grid and the information in the table to draw a histogram for the worm length data. Be sure to label the axes of your histogram.

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• Based on the histogram, what is a typical length for these 25 earthworms? Explain how you know.
• Write 1–2 sentences to describe the spread of the data. Do most of the worms have a length that is close to your estimate of a typical length, or are they very different in length?

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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.

Measuring Earthworms

Unit 8 ● Lesson 7 ● Activity 2

• In a histogram, are we able to see clusters of values in the distribution?
• Can we see the largest and smallest values? Can we tell the overall spread?
• How do we identify the center of a distribution?

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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.

Tall and Taller Players

Unit 8 ● Lesson 7 ● Activity 3

Professional basketball players tend to be taller than professional baseball players.

Here are two histograms that show height distributions of 50 male professional baseball players and 50 male professional basketball players.

1. Decide which histogram shows the heights of baseball players and which shows the heights of basketball players. Be prepared to explain your reasoning.

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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.

Tall and Taller Players

Unit 8 ● Lesson 7 ● Activity 3

• Write 2–3 sentences that describe the distribution of the heights of the basketball players. Comment on the center and spread of the data.
• Write 2–3 sentences that describe the distribution of the heights of the baseball players. Comment on the center and spread of the data.

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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 Histograms to Answer Statistical Questions

Unit 8 ● Lesson 7

• What are some decisions we should think about �and make before drawing a histogram?
• Does the width of each bar have to represent a distance of 5 units, or can it represent other number of units?
• What does the horizontal axis of a histogram tell us? What about the vertical axis?
• How do we know how tall to make each bar?

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• How would you describe a typical weight for this group of dogs?
• What can we say about the spread of the dog weights based on this histogram?

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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 7

• I can draw a histogram from a table of data.
• I can use a histogram to describe the distribution of data and determine a typical value for the data.

Learning Targets

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A Tale of Two Seasons

Unit 8 ● Lesson 7 ● Activity 4

The two histograms show the points scored per game by a basketball player in 2008 and 2016.

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1. What is a typical number of points per game scored by this player in 2008? What about in 2016? Explain your reasoning.
2. Write 2–3 sentences that describe the spreads of the two distributions, including what spreads might tell us in this context.

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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.

center

Unit 8 ● Lesson 7

The center of a set of numerical data is a value in the middle of the distribution. It represents a typical value for the data set.

For example, the center of this distribution of cat weights is between 4.5 and 5 kilograms.

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.

distribution

Unit 8 ● Lesson 7

The distribution tells how many times each value occurs in a data set. For example, in the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.

Here is a dot plot that shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35.

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.

frequency

Unit 8 ● Lesson 7

The frequency of a data value is how many times it occurs in the data set.

For example, there were 20 dogs in a park. The table shows the frequency of each color.

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.

histogram

Unit 8 ● Lesson 7

A histogram is a way to represent data on a number line. Data values are grouped by ranges. The height of the bar shows how many data values are in that group.

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This histogram shows there were 10 people who earned 2 or 3 tickets. We can't tell how many of them earned 2 tickets or how many earned 3. Each bar includes the left-end value but not the right-end value. (There were 5 people who earned 0 or 1 tickets and 13 people who earned 6 or 7 tickets.)

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.

spread

Unit 8 ● Lesson 7

The spread of a set of numerical data tells how far apart the values are.

For example, the dot plots show that the travel times for students in South Africa are more spread out than for New Zealand.

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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