# Bivariate Data

## Objective

Calculate relative frequencies in two-way tables to investigate associations in 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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• 6.RP.A.3.C

• 7.RP.A.3

• 7.SP.C.5

## Criteria for Success

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1. Understand relative frequency as the fraction of the frequency of a data value over the total number of data values.
2. Understand that looking only at quantities of data values in a two-way table can be misleading; relative frequencies adjust for this by taking into account the total number of data values.
3. Calculate relative frequencies in two-way tables to determine if there is an association between the variables.

## Tips for Teachers

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• A key question to keep in mind throughout this lesson is, “Does there appear to be an association between the two variables, and if so, then how does relative frequency support your conclusion?” (MP.2).
• The following materials are needed for this lesson: calculators.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

A survey asked a group of people if they play bingo. The results are shown in the two-way table below.

 Play bingo Do not play bingo TOTAL Younger than 30 years 25 150 175 30 years or older 10 2 12 TOTAL 35 152 187
1. Looking at the “Play bingo” column, who appears more likely to play bingo: someone who is younger than 30 years or someone who is 30 years or older?
2. Does this conclusion seem accurate? What information in the table suggests that this conclusion might not be accurate?

### Problem 2

Use the data in the two-way table from Anchor Problem #1 to calculate the row relative frequencies. Write them in the blank table below.

 Play bingo Do not play bingo TOTAL Younger than 30 years 30 years or older TOTAL n/a n/a n/a
1. Looking at the relative frequencies, who is more likely to play bingo: someone who is younger than 30 years or someone who is 30 years or older?
2. How did finding the relative frequencies give you a more accurate view of the data to make a better conclusion?

### Problem 3

A sample of 400 participants (teachers and students) were randomly selected from the middle schools in Boston. They were asked which type of movie they preferred: action, drama, science fiction, or comedy. The results are shown in the two-way table below.

 Movie Preference Action Drama Science Fiction Comedy Total Student 120 60 30 90 300 Teacher 40 20 10 30 100 Total 160 80 40 120 400
1. Calculate the row relative frequency and write them in the two-way table below.
 Movie Preference Action Drama Science Fiction Comedy Total Student Teacher Total
1. Who is more likely, teachers or students, to prefer action movies? Comedy movies?
2. Is the participant’s status (teacher or student) related to what type of movie he or she prefers to watch?
3. What does it mean when we say there is no association between two variables? Explain.

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic D > Lesson 14Example 2 and Exercises 4-5

Grade 8 Mathematics > Module 6 > Topic D > Lesson 14 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.

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All the students at a middle school were asked to identify their favorite academic subject and whether they were in the 7th grade or 8th grade. Here are the results: