Bivariate Data

Lesson 2

Objective

Create scatter plots for data sets and make observations about the data.

Common Core Standards

Core Standards

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  • 8.SP.A.1 — Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Foundational Standards

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  • 6.SP.B.4

Criteria for Success

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  1. Create a scatter plot for a set of data with appropriate scales and labels for the axes.
  2. Understand a statistical relationship is not the same as a causal relationship; if two variables have a statistical relationship, it does not mean that they also have a causal relationship. 
  3. Make observations of bivariate data shown in scatter plots. 

Tips for Teachers

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  • The following materials are helpful for this lesson: graph paper.
  • A common misconception is to confuse causality with association. For example, students may misunderstand a relationship between two variables to imply that one variable causes another to change, when there is only evidence to show an association between the two variables. As students describe relationships between variables, ensure they use language to imply an association rather than a casual relationship (MP.6).

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Anchor Problems

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Problem 1

Do taller people tend to have bigger hands?

Option 1: Collect data measurements.

  • Students measure their hand spans in centimeters and heights in inches. 
  • Record the values in a table.

Option 2: Use predetermined data measurements.

  • Use the hypothetical data set provided here by Illustrative Mathematics.
  • Students can also model one or two measurements in front of the whole class and add that data to the table.
  1. Create a clearly labeled graph that displays the relationship between height and hand span. 
  2. Based on the graph, how would you answer the question about whether taller people tend to have bigger hands?
  3. Do you see a pattern in the scatter plot that indicates a statistical relationship between height and hand span? Explain.
  4. Can you conclude that having a bigger hand span causes people to be taller?

Guiding Questions

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References

Illustrative Mathematics Hand Span and Height

Hand Span and Height, accessed on March 14, 2017, 5:57 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem 2

Is there a relationship between price and the quality of athletic shoes? 

The data in the table below is from the Consumer Reports website. The variable $$x$$  represents the price in dollars, and the variable $$y$$ represents the Consumer Reports quality rating. The quality rating is on a scale of 0 to 100, with 100 being the highest quality.

Shoe Price (dollars) Quality Rating
1 65 71
2 45 70
3 45 62
4 80 59
5 110 58
6 110 57
7 30 56
8 80 52
9 110 51
10 70 51
  1. Construct a scatter plot of the data. 
  2. Does there appear to be a statistical relationship between price and quality rating?
  3. According to your graph, is it true that if shoes have a high price then they must be of high quality?

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic B > Lesson 6Exercises 4-8

Grade 8 Mathematics > Module 6 > Topic B > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Examples where students create scatter plots from various data sets; include data sets where students must determine the most appropriate scale to use

Target Task

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Here is a table that shows measurements of right hand length and right foot length for five people.

  Right hand length (cm) Right foot length (cm)
Person A 19 27
Person B 21 30
Person C 17 23
Person D 18 24
Person E 19 26
  1. Draw a scatter plot for the data.
  2. Circle the point in the scatter plot that represents Person D’s measurements

References

Open Up Resources Grade 8 Unit 6 Lesson 22.4 Right Side Measurements

Grade 8 Unit 6 Lesson 2 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed April 23, 2018, 9:56 a.m..

Mastery Response

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