Whole Earth Curriculum WEC

Lesson 11 — Comparing Distributions

Learners **summarize and compare distributions** of a single variable using plots and summary statistics: they compute center (mean, median), spread (range, interquartile range), and shape (symmetric or skewed), draw box plots, and compare two distributions in words — connecting "average" to questions of who is left out of the average.

D05 P3: Intellectual & Cognitive Awareness D05.S4 55 minutes Draft

Objectives

Essential question

How do I summarize and compare two distributions of a single variable using plots and summary statistics?

distributionhistogrambox plotmeanmedianinterquartile rangeshapespread

Materials

Standard materials

Low-tech / no-cost

Enriched / lab & device

Works in different contexts

Two box plots side by side on the same scale, both with the same center (mean and median 11) but very different spread — one tight and symmetric, one wide with long tails — with the median, quartiles, and range labeled, plus a note comparing center, spread, and shape
Two box plots side by side on the same scale, both with the same center (mean and median 11) but very different spread — one tight and symmetric, one wide with long tails — with the median, quartiles, and range labeled, plus a note comparing center, spread, and shape

Lesson 11 — Comparing Distributions

Summary

Learners summarize and compare distributions of a single variable using plots and summary statistics: they compute center (mean, median), spread (range, interquartile range), and shape (symmetric or skewed), draw box plots, and compare two distributions in words — connecting “average” to questions of who is left out of the average.

Objectives

  • Summarize and compare distributions of a single variable using plots and summary statistics. (D05.S4.09.01)

Connection

“Average” hides almost everything. Two neighborhoods can have the same average commute time while one is a tight cluster of ten-minute trips and the other is a wild spread from five minutes to two hours. A single number cannot show that difference — you need center (where the middle is), spread (how far the data reaches), and shape (whether it leans). Today you learn to describe and compare a whole distribution, so “average” stops hiding the people at the edges.

Materials

  • Comparison sheet
  • Worked-example card

Preparation

  • Copy the comparison sheet and worked-example card.
  • Retrieval: from Grades 6–8, recall mean, median, range, and reading a box plot.

Facilitator note

This lesson is written to the learner (“you”). The skill to land: summarize a distribution with center (mean, median), spread (range, interquartile range), and shape (symmetric or skewed), and compare two distributions using all three. Use a worked example first (S-011): two small data sets with the same mean but very different spreads and shapes, summarized side by side. The critical-thinking lens: one summary number (the mean) is not “the answer” — a distribution is the whole picture, and you must say which measure of center fits a skewed shape (median, not mean). The egalitarian lens: the mean hides the people at the edges; describing spread and shape is how data tells you who is left out — the same idea behind honest reporting on income, health, and access (S-006). The global lens: comparing distributions is the same act everywhere — two seasons of rainfall, two regions’ harvests, two groups’ test scores — and it is the first step from “numbers” to “questions.” The ethics lens: reporting only the “average” when the spread tells a different story is a form of dishonesty — honest data work means showing center, spread, and shape, not picking the number that flatters (philosophy §5). The technology & environment lens: software draws a box plot in a moment, but the human must choose which measure of center is honest for a skewed shape; and distributions of rainfall, temperature, and harvest describe the environment we depend on. Keep it grounded in real, small data the learner can sort by hand.

Procedure

  1. Recall (5 min). From Grades 6–8: what is the median? The range? What does a box plot show?
  2. Meet the three descriptors (8 min). Center = where the middle is (mean, median). Spread = how far the data reaches (range, interquartile range). Shape = whether it is symmetric or skewed (leans left or right).
  3. Study the worked example (12 min). Data set A: 9, 10, 10, 11, 11, 11, 12, 12, 13. Data set B: 2, 4, 6, 10, 11, 11, 12, 19, 24. Both have mean 11 — but A is tightly clustered (range 4) and symmetric, while B is spread wide (range 22) with long tails. Write the comparison: “Same center, very different spread.”
  4. Compute and draw (15 min). On the comparison sheet, for two new data sets (two neighborhoods’ commute times in minutes), compute the median, mean, range, and IQR, and draw a box plot for each.
  5. Compare in words (10 min). Write a two-sentence comparison naming center, spread, and shape. Which neighborhood’s “average” hides more variety? Whose experience does the mean not represent?
  6. Close (5 min). Center, spread, shape — three words that keep “average” honest.

Differentiation

  • Support: Provide the five-number summary pre-computed and ask learners to draw the box plots and write the comparison.
  • Extension: Add one extreme outlier to a data set and explain, with numbers, why the mean moves but the median barely does.

Assessment

  • Formative (observation): Can the learner compute center and spread and write a comparison that names center, spread, and shape?
  • Portfolio artifact: The completed comparison sheet with two box plots, kept in the portfolio.

Home connection

Collect one small set of real numbers at home (ages of people you know, prices at a market, times of a repeated trip). Compute the median and range and describe the shape in one sentence.

Resources