Unit 2, Lesson 1 : Introducing Relationships and Representing Categorical Variables

Introducing Relationships and Representing Categorical Variables

Unit 2, Topics 2.1–2.2: Introducing Relationships and Representing Categorical Variables

Overview

This lesson introduces relationships between two categorical variables (like gender and favorite sport) and how to represent them with tables and graphs. Apparent patterns might be real associations or just chance. Context, like who the data is from, matters because it explains possible links. For example, more males liking soccer could reflect cultural trends in a teen survey.

Two categorical variables group data into labels (e.g., yes/no, colors). We’ll use two-way tables for summaries and side-by-side or segmented bar graphs to compare distributions and spot associations.

Assignment:

Part 1: Guided Practice Activity

Work on your own. Use the data below from 20 students (from a class survey). Identify a question and represent the two categorical variables.

Data:

• Gender: Male, Female, Male, Female, Male, Male, Female, Male, Female, Male, Female, Male, Male, Female, Male, Female, Male, Female, Male, Male
• Favorite Sport: Soccer, Basketball, Soccer, Tennis, Soccer, Basketball, Tennis, Soccer, Basketball, Tennis, Soccer, Basketball, Soccer, Tennis, Basketball, Soccer, Tennis, Basketball, Soccer, Tennis

Tasks:

1. Identifying Questions and Tables:
   • Write 1 question about possible relationships (e.g., "Is soccer more popular for males?").
   • Create a two-way table (contingency table) with frequency counts (rows: Gender, columns: Sport).
   • Calculate joint relative frequencies (cell count divided by total, e.g., Male-Soccer / 20).
   • Write 1-2 sentences about associations (e.g., "Higher joint frequency for males and soccer suggests a link.").
   • Extra Practice: Use your own data (e.g., "Pet Ownership: Yes/No" and "Favorite Color: Red/Blue" from 5 people). Make a two-way table.
2. Graphical Representations:
   • Sketch a side-by-side bar graph (bars for each sport grouped by gender, heights for counts).
   • Sketch a segmented bar graph (bars for gender, segments for sports).
   • Write 1-2 sentences comparing distributions (e.g., "Males have more soccer bars, showing stronger association.").
   • Extra Practice: Sketch a side-by-side bar for your "Pet Ownership" data.
3. Reflection:
   • Write 2-3 sentences noting if patterns seem random or real, using context (e.g., "The soccer-male link might be real in teens due to school teams, not chance.").

Part 2: Independent Practice

Use this data from 16 students:

• Exercise Level: High, Low, High, Low, High, High, Low, High, Low, High, High, Low, High, Low, High, High
• Favorite Drink: Water, Soda, Water, Soda, Water, Soda, Water, Water, Soda, Water, Water, Soda, Water, Soda, Water, Water

Tasks:

• Write a question about relationships 
• Create a two-way table with joint relative frequencies.
• Sketch side-by-side and segmented bar graphs.
• Write 2-3 sentences comparing distributions and justifying an association claim with context 
• Extra Activity: Invent data for two variables. Make a table and graphs, compare, and claim with context.

Homework Assignment

• Collect data from 5 people on two categorical variables. Make a two-way table, sketch bar graphs, compare distributions, and justify a claim with context to share next class.