# MA.912.DP.3.1

Construct a two-way frequency table summarizing bivariate categorical data. Interpret joint and marginal frequencies and determine possible associations in terms of a real-world context.

### Examples

Algebra 1 Example: Complete the frequency table below.

 Has an A in math Doesn't have an A in math Total Plays an instrument 20 90 Doesn't play an instrument 20 Total 350

Using the information in the table, it is possible to determine that the second column contains the numbers 70 and 240. This means that there are 70 students who play an instrument but do not have an A in math and the total number of students who play an instrument is 90. The ratio of the joint frequencies in the first column is 1 to 1 and the ratio in the second column is 7 to 24, indicating a strong positive association between playing an instrument and getting an A in math.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200380: Algebra 1-B (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))
7912090: Access Algebra 1B (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200385: Algebra 1-B for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))
7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.DP.3.AP.1: When given a two-way frequency table summarizing bivariate categorical data, identify joint and marginal frequencies.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Two-Way Relative Frequency Table:

Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

Type: Formative Assessment

Music and Sports:

Students are asked to construct a two-way frequency table given a set of raw data.

Type: Formative Assessment

Marginal and Joint Frequency:

Students are asked to use a two-way frequency table to interpret marginal and joint relative frequencies.

Type: Formative Assessment

Who Is a Vegetarian?:

Students are given a two-way frequency table and asked to determine if there is a relationship between the two variables.

Type: Formative Assessment

Breakfast Drink Preference:

Students are asked to use data from a survey to create a two-way frequency table.

Type: Formative Assessment

## Lesson Plan

Two-Way Math Survey:

In this lesson, students will construct a two-way table based on data given. They will interpret the data to find if there is a correlation between the two variables from the same subject. As the lesson progresses, students will create their own testable questions that they will collect data on using the survey method. Students will show their mastery of this math concept with the presentation of the data in a two-way table and interpretation of the data to draw inferences.

Type: Lesson Plan

## MFAS Formative Assessments

Breakfast Drink Preference:

Students are asked to use data from a survey to create a two-way frequency table.

Marginal and Joint Frequency:

Students are asked to use a two-way frequency table to interpret marginal and joint relative frequencies.

Music and Sports:

Students are asked to construct a two-way frequency table given a set of raw data.

Two-Way Relative Frequency Table:

Students are asked to convert raw data to relative frequencies by both rows and columns given a two-way frequency table.

Who Is a Vegetarian?:

Students are given a two-way frequency table and asked to determine if there is a relationship between the two variables.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.