Bivariate Data

Lesson 9

Math

Unit 8

8th Grade

Lesson 9 of 9

Objective


Complete two-way tables and identify associations in the 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.C.5

Criteria for Success


  1. Complete partially filled-in two-way tables using information in the problem.
  2. Use relative frequencies to determine if two variables are associated. 
  3. Understand that if relative frequencies are about the same for either rows or columns, then it is reasonable to say that there is no association between the two variables.

Tips for Teachers


Lesson Materials

  • Calculators (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

A survey asked a sample of residents of Boston and Worcester how many languages they spoke. The table below shows some of the data. 

  1 language 2 languages 3 or more languages Total
Boston 84   9 150
Worcester   18 5  
Total   75   230

a.   Complete the table and calculate the row relative frequency. Fill in the new table below.

  1 language 2 languages 3 or more languages Total
  # Frequency # Frequency # Frequency  
Boston 84       9   150
Worcester     18   5    
Total     75       230

b.   Based on the data in the new table, which of the following statements are accurate? Select all that apply.

  1. a.   More people from Boston were surveyed than people from Worcester.

  2. b.   More than 50% of all those surveyed speak only 1 language.

  3. c.   A higher proportion of Worcester residents speak 2 languages than Boston residents.

  4. d.   If a person from Boston is randomly selected, there is a higher likelihood that this person speaks 2 languages than 1 language.

  5. e.   If a person who speaks 3 or more languages is randomly selected, there is a higher likelihood that this person is from Boston than from Worcester.

Guiding Questions

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Student Response

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Problem 2

An incomplete two-way table is shown below. 

  Prefer to exercise alone Prefer to exercise with a group
Teenagers (<18 y.o.) 30 60
Adults (>18 y.o) 12  

Of the numbers 4, 24, or 60, which number could you put in the missing cell in order to indicate:

  1. No association between preference of exercise company and age
  2. A preference of adults to exercise alone compared to teenagers
  3. A preference of adults to exercise with a group compared to teenagers

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


A student knew a lot of classmates who liked to listen to music when they studied. They were curious if this had an impact on test performance, so the student conducted a random sample of 100 of their peers asking them if they listened to music when they studied and if they met their goal on their last math test. The results are described below.

  • 64 students listen to music when they study
  • 27 students do not listen to music and met their goal on this math test
  • 15 students listen to music when they study and did not meet their goal on their math test
  • 24 students did not meet their goal on their math test

a.   Create a two-way table to represent the information. Label the rows as Listens to music and Does not listen to music. Include both the number of students in each cell, as well as the row relative frequency rounded to the nearest percent.

b.   Is there evidence of association between the variables suggesting that listening to music has an impact on test performance? Justify your response.

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.

  • Examples where students are given partial information in a two-way table and must complete the rest of the data
  • Examples similar to Anchor Problem #2, where students must create two-way tables that indicate various types of associations
  • Error analysis problems and/or critique others’ reasoning where students must determine the validity of a conclusion and support their reasoning using evidence from the table

Lesson Map

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