Bivariate Data

Lesson 7

Math

Unit 8

8th Grade

Lesson 7 of 9

Objective


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

Common Core Standards


Core Standards

  • 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?

Foundational Standards

  • 7.SP.A.1
  • 7.SP.A.2

Criteria for Success


  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


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


Problem 1

A double bar graph and a segmented bar graph are shown below, representing the same data set. 

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

a.   Name two things you notice and two things you wonder about.

b.   How many people did the reporter survey?

c.   How many people in the age group of 16–30 years old were against the increase in minimum wage?

d.   Were more people in favor of the increase or against the increase?

Guiding Questions

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Problem 3

Marlo takes the bus to school. He notices that the bus tends to arrive late to school when it is raining. Marlo decides to investigate the timeliness of the buses based on the morning weather. He records answers to the following questions each school morning for the entire 180-day school year: 

  • In the morning, what is the weather: rain/snow or no precipitation?
  • When does the bus arrive at school: on time or late?

Some highlights of Marlo's results: 

  • Of the 139 days the bus arrived on time, it rained or snowed on 36 of those days.
  • Of the 118 days with no precipitation, the bus arrived late on 15 of those days.
  • It rained or snowed on 62 days. 

a.   Draw a two-way frequency table to summarize the data.

b.   Of all the school days, what proportion did the bus arrive on time?

c.   Of all the school days, what proportion did the bus arrive on time when there was no precipitation?

d.   Of the days it rained or snowed, what proportion did the bus arrive late?

e.   Of the days the bus arrived late, what proportion did it rain or snow?

f.   On a day of school without precipitation, would you predict the bus to be on time or late? Explain your reasoning.

Guiding Questions

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Problem Set

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Target Task


A random group of 6th and 8th grade students at a school are asked the question: Do you prefer to complete your homework on a computer or on paper?

  • Of the 56 sixth graders, 18 answered computer and 38 answered paper.
  • Of the 60 eighth graders, 52 answered computer and 8 answered paper.

a.   Create a two-way table to represent the data. Label your rows as 6th graders and 8th graders.

b.   What is the proportion, of all of the students, who are in 8th grade and prefer to complete their homework on a computer?

c.   Of the students who prefer to complete their homework on paper, what proportion are in 6th grade?

d.   A student is selected at random from either the 6th or 8th grade at this school. What do you predict is this student's  preferred method of completing their homework? Explain your reasoning. 

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or 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 SportsOption to either survey the class and collect the data or use the sample data on the website
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Lesson 6

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Lesson 8

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