Lesson 1 — Reading Data: Mean and Range

Summary

Learners compute the mean (a central value) and the range (a measure of spread) for small datasets, see how a single outlier pulls the mean, and ask what any one number leaves out. This is the unit’s opening statistical toolkit — the same mean and range they will use when they analyze data about inheritance, energy, climate, and the cosmos in later lessons.

Objectives

• Analyze data using basic statistics — mean, range, and trend — and assess how well the data support a conclusion. (D06.S1.10.01)

Connection

If someone asks, “how much rain does your town get?” you could list every day of the year — or you could give one number, the mean, that stands in for the whole batch. But one number always hides something: two towns can have the same mean rainfall while one is steady drizzle and the other swings between drought and flood. The range catches that swing — the gap between the smallest and largest values. Mean and range together are the first honest way to summarize numbers without pretending one number tells the whole story.

Materials

• Mean-and-range worksheet
• Science journal

Preparation

• Copy or draw the mean-and-range worksheet (the worked rainfall example below).
• Retrieval: from Grade 8 and 9, tables, bar graphs, and organizing data (D06.S1.06.01, D06.S1.09.01). Today we add two numeric summaries: mean and range.
• Prepare one worked example and three practice sets.

Facilitator note

This lesson is written to the learner (“you”). The idea to land: the mean is a central value (sum ÷ count); the range is a spread (largest − smallest); and a single outlier pulls the mean away from the typical value, while the range is exactly what catches that spread. Teach the computation with a worked example first — for a procedural skill like this, explicit instruction with guided practice beats discovery (S-011). Then let learners compute, self-check, and check each other.

The critical-thinking lens: every summary is a choice — what did the person choose to show, and what did they leave out? The ethics lens: numbers are used to make decisions about people; an average that hides the poorest or the most affected is a moral problem, not just a math one. The egalitarian lens: the mean and range are free, shared tools — any person, anywhere, can use them to read claims made about their own community, not be read by them. The global lens: the same two numbers work whether the data is rainfall in a monsoon region, a harvest in a dryland farm, or a fever chart in a clinic. Preview: Lesson 2 turns to trend — how well a whole dataset supports a conclusion.

Procedure

1. Recall (5 min). From Grade 9: what are the parts of a data table, and how do you turn numbers into a bar graph? Name one time you saw a single number used to describe many numbers (a “average” in a news story, a score, a price).
2. Meet the mean and range (15 min). Here is a town’s daily rainfall in millimetres over seven days: 3, 5, 4, 40, 6, 5, 4.
   • Mean: add them (3+5+4+40+6+5+4 = 67), divide by 7 → 67 ÷ 7 ≈ 9.6 mm.
   • Range: largest − smallest = 40 − 3 = 37 mm. Notice the outlier, 40, pulls the mean up to 9.6 — higher than six of the seven days. The range (37) is what exposes the one very wet day.
3. Guided practice (15 min). With a partner, compute mean and range for three small sets (e.g., 4, 5, 6, 5, 4; then 2, 2, 2, 18, 2; then 10, 12, 11, 10). For each, write sum ÷ count and largest − smallest. Compare answers and agree before moving on.
4. Independent practice (15 min). In your journal, compute mean and range for a set of eight numbers of your own (heights in your group, days of rain you remember, or any real numbers). Then remove the largest value and recompute the mean — how far did it move? Mark anything unsure with “not yet” and try again.
5. Close (5 min). In one sentence: what does the mean capture, what does the range capture, and what does a single outlier do to the mean?

Differentiation

• Support: Use physical counters and share them equally to “see” the mean; give a pre-written sum to complete.
• Extension: Compare two towns with the same mean but very different ranges, and explain which is easier to plan a reservoir for, and why.

Assessment

• Formative (peer + self): Can the learner compute mean and range correctly, and explain how an outlier moves the mean?
• Portfolio artifact (unit): The completed worksheet with the “what the mean hides” reflection, as the first page of the unit’s data-and-evidence toolkit.

Home connection

Ask someone at home: what “average” numbers do you meet in a week — prices, scores, weather? Compute the mean and range of one small set together, and ask what that average might be hiding.

Resources

• On the use of worked examples and guided practice for novice skills: Kirschner, Sweller & Clark (2006), https://doi.org/10.1207/s15326985ep4102_1 (S-011).
• On descriptive statistics (mean, median, range) as background: Encyclopaedia Britannica, “Probability and statistics,” https://www.britannica.com/science/probability (S-301).