Unit 1 Lesson 9 : Comparing Distributions of Quantitative Variables

Comparing Distributions of Quantitative Variables

Unit 1, Topic 1.9: Comparing Distributions of Quantitative Variables

Overview

This lesson focuses on comparing two or more sets of quantitative data (like test scores for two classes) by looking at their shape, center, spread, and odd features. Side-by-side graphs help us see differences. Context, like who the groups are, matters because it explains why distributions vary. For example, comparing "scores" for freshmen vs. seniors needs context about experience levels.

Quantitative data uses numbers to measure amounts (e.g., time, weight). We’ll use side-by-side boxplots or histograms to compare, then justify claims about relative positions (e.g., one group has a higher middle).

Assignment:

Part 1: Guided Practice Activity

Work on your own. Use the datasets below from two classes (from a school survey). Compare their distributions.

Dataset A (Class 1 Test Scores): 55, 60, 65, 68, 72, 75, 78, 80, 82, 85 Dataset B (Class 2 Test Scores): 70, 75, 78, 80, 82, 85, 87, 90, 92, 95

Tasks:

1. Creating Side-by-Side Graphs:
   • Sketch side-by-side histograms or boxplots (group into intervals for histograms or use five-number summary for boxplots; draw by hand, e.g., Class A box: min 55, Q1 65, median 76.5, Q3 80, max 85; Class B: min 70, Q1 77.5, median 83.5, Q3 90.5, max 95).
   • Write 1-2 sentences about how the graphs help compare (e.g., "Side-by-side boxplots show Class B's higher median.").
   • Extra Practice: Use your own data (e.g., "Heights for two groups" from 5 people each). Sketch side-by-side boxplots and note differences.
2. Comparing Distributions:
   • Compare shape, center, variability, and unusual features (e.g., "Class A is skewed right with lower center; Class B is symmetric with smaller spread.").
   • Write 1-2 sentences justifying a relative position claim with context (e.g., "Class B has a higher median of 83.5 vs. 76.5, possibly because it's advanced students.").
   • Extra Practice: Compare your "Heights" datasets and justify a claim.

Part 2: Independent Practice

Compare these datasets from two survey groups: Group A (Commute Times, minutes): 10, 15, 20, 25, 30, 35, 40 Group B (Commute Times, minutes): 20, 25, 30, 35, 40, 45, 60

Tasks:

• Sketch side-by-side boxplots (find five-number summaries: Group A min 10, Q1 17.5, median 25, Q3 35, max 40; Group B min 20, Q1 25, median 35, Q3 45, max 60).
• Compare shape, center, variability, and unusual features, using units.
• Write 2-3 sentences justifying a claim about relative positions in context (e.g., "Group B's median of 35 minutes is higher than Group A's 25, suggesting longer commutes for urban students.").
• Extra Activity: Invent datasets for two groups (e.g., "Study Hours for two classes"). Sketch side-by-side histograms, compare distributions, and justify a claim.

Homework Assignment

• Collect two small datasets (e.g., sleep hours for weekdays vs. weekends from 5 people). Sketch side-by-side boxplots, compare distributions, and justify a claim with context to share next class.