# Bivariate Data

## Objective

Create and analyze two-way tables representing bivariate categorical data.

## Common Core Standards

### Core Standards

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• 8.SP.A.4 — Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

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• 7.SP.A.1

• 7.SP.A.2

## Criteria for Success

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1. Analyze and interpret forms of categorical displays, including double bar graphs, segmented bar graphs, and two-way tables
2. Create a two-way frequency table to represent categorical data in two variables.
3. Interpret two-way frequency tables using proportional reasoning.

## Tips for Teachers

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Prior to this lesson, it may be valuable to review univariate data and representative samples from seventh gade. A good resource for this is Exercises 1–8 from EngageNY, Grade 8, Module 6, Lesson 13.

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## Anchor Problems

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### Problem 1

A double bar graph and a segmented bar graph are shown below.

For each graph, name two things you notice and two things you wonder about.

#### Guiding Questions

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#### References

Open Up Resources Grade 8 Unit 6 Lesson 9Image from Lesson 9.2: Matching Representations Card Sort

Grade 8 Unit 6 Lesson 9 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 20, 2018, 4:12 p.m..

### Problem 2

A reporter in a small town polled some residents and asked them if they were in favor of increasing the minimum wage or against it. The two-way table summarizes the data.

 In favor of increase Against increase TOTAL 16-30 years old 42 16 58 31-50 years old 28 36 64 TOTAL 70 52 112
1. Name two things you notice and two things you wonder about.
2. How many people did the reporter survey?
3. How many people in the age group of 16–30 years old were against the increase in minimum wage?
4. Were more people in favor of the increase or against the increase?

#### Guiding Questions

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### Problem 3

A student is investigating the favorite ice-cream flavors of girls and boys at school. She asks the following two questions to her classmates:

• Which of the following ice-cream flavors is your favorite: chocolate, strawberry, or vanilla?
• Which is your gender: male or female?

The results of the survey are as follows:

• Of the 30 students who prefer chocolate, 22 are males.
• Of the 25 students who prefer strawberry, 15 are females.
• Of the 27 students who prefer vanilla, 13 are males.
1. Draw a two-way frequency table to summarize the data.
2. Of all the students, what proportion preferred chocolate?
3. Of all the students, what proportion were females who preferred vanilla?
4. Of the female students, what proportion preferred strawberry?
5. Of the students who preferred vanilla, what proportion were male?
6. A student is selected at random from the school. What would you predict this student’s favorite ice-cream flavor to be?
7. Suppose this student is female. What would you predict her favorite ice-cream flavor to be?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic D > Lesson 13Examples 2 and 3

Grade 8 Mathematics > Module 6 > Topic D > Lesson 13 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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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

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

• Challenge: Design a survey to collect bivariate data from your peers. Organize your results in a two-way table and make 3 observations of the data based on your table.
• EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic D > Lesson 13Problem Set; note, problems in the problem set reference “relative frequency,” which is not defined until Lesson 8. Students should still be able to answer these questions as they also ask for “proportion,” which is used in this lesson.
• Illustrative Mathematics Music and SportsLines up with Anchor Problems #3 and #4 nicely; option to either survey the class and collect the data or use the sample data on the website

## Target Task

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A random group of students are polled about how they get to school by walking, riding the bus, or carpooling.

• Of the 44 male students polled, 9 of them walk and 26 of them ride the bus.
• Of the 58 female students, 26 of them ride the bus and 24 of them carpool.
1. Create a two-way table to represent the data. Label your rows as Male and Female.
2. What is the proportion of all of the students, who are female and walk to school?
3. Of the students who carpool, what proportion are female?
4. A student is selected at random from this school. What would you predict this student’s mode of school transportation to be? Explain your answer.

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic D > Lesson 13Exit Ticket

Grade 8 Mathematics > Module 6 > Topic D > Lesson 13 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.

### Mastery Response

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