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Teacher guide — Grade 8, Unit 5: Summarising data

Time: 3 lessons + project (about 5 periods). Track: A (no-code).

# Lesson Time
1 Mean, median and mode 40–45 min
2 Which summary when? 40–45 min
3 Spread and what summaries hide 40–45 min
P Unit project: What's typical in our class? 2 periods

Before you start

  • Materials: Calculator, strips of paper for the human-median activity.
  • Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet

All eight units run on paper, calculators and the blackboard. Computers are optional (spreadsheet or CODAP, https://codap.concord.org); every activity below has a paper version.

Common misconceptions

  • The mean is always the best 'average'. One extreme value can drag it.
  • The mode is the 'biggest' value. It is the most frequent.

Differentiation

  • Support: give a partially filled table / sentence starters; pair with a data-steward role.
  • Stretch: ask "what would change your conclusion?" and "who is missing?"

Answer key (check questions)

Lesson 1: Mean, median and mode 1. Mean of 20, 20, 30, 40, 90?
Answer: 200 ÷ 5 = 40. 2. Median of 20, 20, 30, 40, 90?
Answer: 30. 3. Mode and range?
Answer: Mode 20; range 90 − 20 = 70.

Lesson 2: Which summary when? 1. Incomes: 9 × 15,000 and 1 × 300,000 — mean?
Answer: (135,000 + 300,000) ÷ 10 = 43,500. 2. Median of the same list?
Answer: 15,000. 3. Which is more typical and why?
Answer: The median: the mean is pulled up by one outlier.

Lesson 3: Spread and what summaries hide 1. Mean of class A (7, 8, 8, 9)?
Answer: 8. 2. Mean and range of class B (5, 6, 10, 11)?
Answer: Mean 8; range 6. 3. What do these tell us that the means alone do not?
Answer: B is much more spread out.

Assessment

Starter quiz each lesson (3 questions, one recalling the previous lesson); unit quiz in quiz.yml; project marked with the rubric in docs/pedagogy/assessment.md; 2-minute oral check per group.

Alignment

Extends the Grade 8 compulsory Maths statistics chapter (pie chart, mean, median, mode) with question-forming, data collection and interpretation.

Answers: practice exercises

  1. Mean 47 ÷ 6 ≈ 7.83; median (7 + 8) ÷ 2 = 7.5; mode 7; range 12 − 4 = 8.
  2. Sorted: 12, 19, 22, 27, 31, 38, 45 → median 27. Students who skip sorting take the unsorted middle value, 19.
  3. Maths (12). Favourite subject is categorical: there is no sum of subjects.
  4. Total must be 6 × 15 = 90; known marks sum to 76; missing mark = 14.
  5. Mean = 11,350 ÷ 7 ≈ Rs 1,621; median = Rs 900. The median: six of seven workers earn ≤ 1,000.
  6. Mean 3.8 mm, median 0 mm, mode 0 mm. Tell the planner "most days are dry (median/mode 0), but expect one or two wet days; one day had 35 mm". The mean alone suggests light rain every day, which is wrong.
  7. Any five numbers summing to 50 with middle value 8, e.g. 5, 6, 8, 10, 21.
  8. Example: "Heights centre around 155 cm (median 155, mean 155.4); they spread from 139 to 171 cm (range 32 cm); the distribution is roughly symmetric (mean ≈ median) with no outliers."
  9. Land ownership is right-skewed: a few large landowners raise the mean; many households own much less than the mean (and some own none). The median would describe a typical household better.
  10. e.g. (i) every student improved a little; (ii) most stayed the same but some low scorers improved a lot; (iii) the weakest students left the school or did not sit the exam (a selection effect: the "improvement" is not real).

Real-data exercises: notes

  • R1 Annual totals vary from under 500 mm in the rain-shadow north-west (e.g. Jomsom/Mustang area) to more than 3,500–4,000 mm around Pokhara/Lumle; the distribution is right-skewed with high outliers that are real.
  • R2 Median 4.4, modes 4.0 and 4.3 (bimodal), mean ≈ 4.48 on the 2026-10-11 download (304 events); the mean is above the median because of the right skew from the large events. Accept nearby answers if the file differs.
  • R3 Vegetable prices move with the seasons and with festivals; answers depend on the weeks chosen, so let students compare their weeks rather than expect one right answer. Check that units (Rs/kg) are written.