Learn on PengiBig Ideas Math, Advanced 2Chapter 9: Data Analysis and Displays

Section 9.3: Two-Way Tables

In this Grade 7 lesson from Big Ideas Math Advanced 2, Chapter 9, students learn how to read and make two-way tables to display and analyze two categories of data collected from the same source. Students work with joint frequencies, which are the individual entries in the table, and marginal frequencies, which are the row and column sums that reveal totals across each category. The lesson builds data analysis skills by having students interpret real-world surveys and draw conclusions from the organized data.

Section 1

Reading Joint Frequencies from Two-Way Tables

Property

A joint frequency is the value found at the intersection of a specific row and column in a two-way table, representing the count of data that belongs to both categories simultaneously.

Examples

Section 2

The Anatomy of a Two-Way Table

Property

A two-way table organizes data by showing the relationship between two categorical variables. The table displays frequencies or counts for each combination of categories, with rows representing one variable and columns representing another. Each cell contains the count for that specific combination of categories.

Examples

  • A school surveyed 150 students about ticket preferences, organizing the data with ticket type (Adult, Student) in columns and the count for each type in a row.
  • A stamp collection of 20 stamps has 10 that are 50-cent stamps and 10 that are 80-cent stamps. A two-way table organizes this with stamp type as one variable and quantity as another.
  • A concert venue tracked 500 ticket sales, selling 250 VIP tickets and 250 general admission tickets. This is displayed with ticket type in columns and the number sold in corresponding cells.

Explanation

Two-way tables help visualize relationships between categorical variables by organizing data into rows and columns. Each cell represents a specific combination of the two variables being studied, making it easy to compare frequencies and identify patterns in the data.

Section 3

Calculate marginal frequencies in two-way tables

Property

Marginal frequencies are the totals for each row and column in a two-way table. Row marginal frequency = sum of all entries in that row. Column marginal frequency = sum of all entries in that column.

Examples

Book overview

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Chapter 9: Data Analysis and Displays

  1. Lesson 1

    Section 9.1: Scatter Plots

  2. Lesson 2

    Section 9.2: Lines of Fit

  3. Lesson 3Current

    Section 9.3: Two-Way Tables

  4. Lesson 4

    Section 9.4: Choosing a Data Display

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Reading Joint Frequencies from Two-Way Tables

Property

A joint frequency is the value found at the intersection of a specific row and column in a two-way table, representing the count of data that belongs to both categories simultaneously.

Examples

Section 2

The Anatomy of a Two-Way Table

Property

A two-way table organizes data by showing the relationship between two categorical variables. The table displays frequencies or counts for each combination of categories, with rows representing one variable and columns representing another. Each cell contains the count for that specific combination of categories.

Examples

  • A school surveyed 150 students about ticket preferences, organizing the data with ticket type (Adult, Student) in columns and the count for each type in a row.
  • A stamp collection of 20 stamps has 10 that are 50-cent stamps and 10 that are 80-cent stamps. A two-way table organizes this with stamp type as one variable and quantity as another.
  • A concert venue tracked 500 ticket sales, selling 250 VIP tickets and 250 general admission tickets. This is displayed with ticket type in columns and the number sold in corresponding cells.

Explanation

Two-way tables help visualize relationships between categorical variables by organizing data into rows and columns. Each cell represents a specific combination of the two variables being studied, making it easy to compare frequencies and identify patterns in the data.

Section 3

Calculate marginal frequencies in two-way tables

Property

Marginal frequencies are the totals for each row and column in a two-way table. Row marginal frequency = sum of all entries in that row. Column marginal frequency = sum of all entries in that column.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 9: Data Analysis and Displays

  1. Lesson 1

    Section 9.1: Scatter Plots

  2. Lesson 2

    Section 9.2: Lines of Fit

  3. Lesson 3Current

    Section 9.3: Two-Way Tables

  4. Lesson 4

    Section 9.4: Choosing a Data Display