Unit Plan 24 (Grade 7 Math): Comparing Two Populations
7th graders compare two numerical data sets using mean, median, MAD, and IQR. They interpret dot and box plots, analyze center, spread, and overlap, and make cautious, data-driven inferences in real-world contexts.
Focus: Compare two numerical data distributions; use measures of center (mean/median) and variability (MAD, IQR) to describe differences.
Grade Level: 7
Subject Area: Mathematics (Statistics & Probability • Data, Variability, Inference)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students learn to compare two numerical data sets using visual displays and summary statistics. They construct and interpret dot plots and box plots, compute measures of center (mean, median) and variability (MAD, IQR), and make informal comparative inferences using clear, cautious language. Emphasis: describing shift in center, spread, and overlap, and explaining what the differences mean in context.
Essential Questions
- What do center (mean/median) and variability (MAD/IQR) tell us about a data set?
- How can we judge whether one group tends to have larger or smaller values than another?
- How do overlap and spread affect our confidence in a comparison?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Create and interpret dot plots and box plots for two populations on the same scale.
- Compute and use median, mean, IQR (Q3 − Q1), and MAD (average absolute deviation from the mean).
- Describe similarities and differences between two distributions by discussing center, spread, and overlap.
- Draw informal comparative inferences, using careful wording (likely, tends to, about, roughly).
- Communicate conclusions with units, context, and notes about variability and sample size.
Standards Alignment — CCSS Grade 7
- 7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities and measure the difference between centers in context.
- 7.SP.4: Use measures of center and variability for numerical data from random samples to draw informal comparative inferences about two populations.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision).
Success Criteria — Student Language
- I can build dot plots or box plots for two groups on the same axis.
- I can find median/mean and IQR/MAD and say what they mean.
- I can describe center, spread, and overlap and explain which group tends to be higher or lower.
- I can make a careful comparison in context using words like likely and about.
- I can include units and mention variability or sample size when I conclude.