Bivariate Data

Objective

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

Criteria for Success

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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

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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 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
1. 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
1. Based on the data in the new table, which of the following statements are accurate? Select all that apply.
1. More people from Boston were surveyed than people from Worcester.
2. More than 50% of all those surveyed speak only 1 language.
3. A higher proportion of Worcester residents speak 2 languages than Boston residents.
4. If a person from Boston is randomly selected, there is a higher likelihood that this person speaks 2 languages than 1 language.
5. 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.

Problem 2

An incomplete two-way table is shown below.

 Prefer to exercise alone Prefer to exercise with a group Men 30 60 Women 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 gender
2. A preference of women to exercise alone compared to men
3. A preference of women to exercise with a group compared to men

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.

• 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

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A random sample of 100 eighth-grade students are asked to record two variables: whether they have a television in their bedrooms and if they passed or failed their last math test. The results of the survey are summarized below:

• 55 students have a television in their bedroom
• 35 students do not have a television in their bedroom and passed their last math test
• 25 students have a television and failed their last math test
• 35 students failed their last math test
1. Complete the two-way table to represent the information. Include both the number of students in each cell as well as the row relative frequency rounded to the nearest percent.
 Pass Fail Total Television in the bedroom No television in the bedroom Total
1. Is there evidence of association between the variables? If so, does this imply there is a cause-and-effect relationship? Explain your reasoning.

References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic D > Lesson 14Exit Ticket

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..

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