Using Data Displays to Find Associations

5 min

Teacher Prep
Setup
2 minutes quiet work time followed by a whole-class discussion.

Narrative

The purpose of this Warm-up is for students to answer questions about relative frequency of items after finding missing information in a two-way table.

Monitor for students who find the percentages for the final two questions using different strategies to share during the whole-class discussion. 

Launch

Give students 2 minutes of quiet work time followed by a whole-class discussion. 

Student Task

For a survey, students in a class answered these questions:

  • Do you play a sport?
  • Do you play a musical instrument?

  1. Here is a two-way table that gives some results from the survey. Complete the table, assuming that all students answered both questions.

    plays instrument does not play instrument total
    plays sport 5 16
    does not play sport
    total 15 25

  2. To the nearest percentage point, what percentage of students who play a sport don’t play a musical instrument?

  3. To the nearest percentage point, what percentage of students who don’t play a sport also don’t play a musical instrument?

Sample Response

  1. plays instrument does not play instrument total
    plays sport 55 1111, since 16−5=1116-5=11. 1616
    does not play sport 55, since 9−4=59-4=5. 44, since 15−11=415-11=4. 99, since 25−16=925-16=9.
    total 1010, since 25−15=1025-15=10. 1515 2525

  2. 69%, since 1116=0.6875\frac{11}{16}=0.6875.

  3. 44%, since 49=0.444...\frac{4}{9}=0.444 . . ..

Activity Synthesis (Teacher Notes)

Ask students to share the missing information they found for the table. Record and display their responses for all to see.

Select previously identified students to explain how they found the percentages for the final 2 questions and what that percentage represents. Select students who:

  1. Find a percentage using the values given (for example, 31%, since 516≈0.31\frac{5}{16} \approx 0.31), then subtract from 100% (for example, 69%, since 100−31=69100 - 31 = 69) to answer the question.
  2. Find the actual values first by subtracting (for example, 16−5=1116 - 5 = 11) then computing the percentage (for example, 69%, since 1116=0.6875\frac{11}{16}=0.6875).

Ask the rest of the class if they agree or disagree with the strategies and give time for any questions they have.

Standards
Addressing
  • 8.SP.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. <em>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?</em>
  • 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. <span>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?</span>

15 min

15 min