Unit 1 Lesson 3: Representing Categorical Data with Graphs

Representing Categorical Data with Graphs

Unit 1, Topic 1.4: Representing Categorical Data with Graphs

What We’re Learning About

Graphs for categorical data (like favorite colors or seasons) show patterns. Graphs help us see which groups are most common or how they compare. Context (like who the data is from) matters because it helps us understand why patterns happen. For example, a graph showing “5 reds” could mean 5 red shirts or 5 red cars without context.

Categorical data groups things into labels (e.g., yes/no, sports). We’ll use bar charts (bars for counts or parts) and pie charts (circles split into parts) to show this data. Variation shows up as differences in bar heights or pie slices, which helps us spot trends.

Part 1: Warm-Up Activity

Here’s a small set of data about favorite pizza toppings from 6 people:

• Pepperoni, Cheese, Pepperoni, Veggie, Cheese, Pepperoni

Wrong Statement: "Pepperoni is everyone’s favorite."

--Assignment:

• Point out what’s wrong with this statement.
• Write 1–2 sentences explaining why context (like who these people are) matters.

Part 2: Guided Practice Activity

Use the data below from 12 students (from a class survey). Make bar and pie charts, then describe patterns.

Data:

• Favorite Sport: Soccer, Basketball, Soccer, Tennis, Basketball, Soccer, Tennis, Basketball, Soccer, Tennis, Basketball, Soccer

Tasks:

1. Making Graphs:
• Create a bar chart showing frequencies (count how many times each sport appears; sketch bars by hand—e.g., Soccer: 4, Basketball: 4, Tennis: 3).
• Create a pie chart showing relative frequencies (turn counts into parts of 12, e.g., Soccer: 4/12; sketch a circle split into parts—graph not provided, draw by hand).
• Write 1–2 sentences about variation (e.g., “Soccer and Basketball are close with 4 each, showing they’re popular.”).
• Extra Practice: Use your own data (e.g., “Favorite Day: Monday, Friday…” from 5 friends). Make a bar chart and explain variation.
2. Describing Patterns:
• Write 1–2 sentences describing a pattern and justifying it with context (e.g., “Tennis is least at 3, maybe because it needs special courts.”).
• Extra Practice: Describe a pattern in your “Favorite Day” bar chart from the extra practice.
3. Reflection:
• Write 2–3 sentences about how graphs show variation and why context (like student interests) matters. (Example: “Graphs show Soccer and Basketball tie at 4, while context suggests teens might like team sports more.”)

Part 3: Independent Practice

Look at this data from a survey of 8 students:

• Movie Genre Preference: Action, Comedy, Action, Drama, Comedy, Action, Drama, Comedy

Tasks:

• Make a bar chart for frequencies and a pie chart for relative frequencies (sketch by hand e.g., Action: 3, Comedy: 3, Drama: 2).
• Write 2–3 sentences describing patterns in the graphs, justifying with context (e.g., “Action and Comedy each have 3, suggesting they’re equally liked, maybe because students enjoy excitement.”).
• Extra Activity: Invent a dataset for 6 people (e.g., “Hobby: Reading, Gaming…”). Make a bar chart and pie chart, explain variation, and write why it could answer a question like “Is gaming more popular than reading?”

Homework Assignment

• Collect data from 5 people on a categorical variable (e.g., favorite animal: Dog, Cat…). Make a bar chart and pie chart (sketch by hand), describe variation, and explain how context helps interpret it to share next class.