Mathematics • Year 8 • Unit 4 • Lesson 10
Range and Outliers in the Real World
Apply the range and outlier reasoning to real situations: factory quality control, sports comparisons, exam results, and weather records — decide when outliers should be flagged or excluded.
1. Word problems
Each problem uses ideas from Lesson 10. Show your working — a single answer with no working only earns half marks.
1.1 — Two classes' exam results. Class A: all scored between 60% and 70%. Class B: scored between 20% and 100%. Both have a mean of 65%.
(a) Find each class's range.
(b) Which class is more consistent?
(c) Why is the mean by itself misleading here? 3 marks
1.2 — Bolt manufacturing. Factory A's bolt diameters (mm): 9.9, 10.0, 10.0, 10.1, 10.1. Factory B's bolt diameters (mm): 8.1, 9.5, 10.0, 10.5, 11.9. Target diameter = 10.0 mm; bolts more than 0.5 mm from target are rejected.
(a) Find each factory's range.
(b) How many of each factory's bolts would be rejected?
(c) Which factory is more reliable for bolt production? Justify in one sentence. 3 marks
1.3 — Daily temperature outlier. A week of daily high temperatures (°C): 22, 23, 25, 24, 22, 38, 23. The 38°C day was a heatwave.
(a) Find the range with and without the outlier (38).
(b) Find the mean with and without the outlier.
(c) Should the outlier be included in a report on "typical weekly temperature"? Justify. 3 marks
1.4 — Class quiz. 9 students score on a 20-mark quiz: 14, 16, 15, 17, 16, 15, 18, 17, 2.
(a) Identify the outlier.
(b) Calculate range with and without the outlier.
(c) Suggest ONE plausible reason a student might have scored 2 (and why the teacher might decide to exclude it). 3 marks
1.5 — News headline. A headline reads: "Average home price in the suburb is $1.6 million." Buried in the article, the median price is $850 000.
(a) Explain why the mean and median are so different.
(b) Which statistic is the headline using, and why is it misleading?
(c) If you were a journalist, what would you report instead? 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A sports analyst says "The range of these athletes' 100 m times is only 0.5 s, so they are very consistent." Another analyst replies: "But there's a 12.0 s value that you forgot — the actual range is 1.8 s." In your own words, explain (i) why the second analyst's correction matters, (ii) how a single outlier can completely change the conclusion about consistency, and (iii) what additional measure you could use to describe spread more reliably. Use the term range in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Two classes' exam results
(a) Class A range = 70 − 60 = 10. Class B range = 100 − 20 = 80.
(b) Class A is far more consistent (range 10 vs 80).
(c) Same mean (65%) hides the fact that Class B is wildly inconsistent — some students need help, others are very strong. The mean alone doesn't capture spread; range is needed.
1.2 — Bolt manufacturing
(a) Factory A range = 10.1 − 9.9 = 0.2 mm. Factory B range = 11.9 − 8.1 = 3.8 mm.
(b) Factory A: 0 rejected (all within 0.5 mm). Factory B: 2 rejected (8.1 is 1.9 mm off; 11.9 is 1.9 mm off).
(c) Factory A — tiny range of 0.2 mm means production is highly consistent and within tolerance; Factory B has 40% rejection rate.
1.3 — Daily temperature outlier
(a) With 38: range = 38 − 22 = 16°C. Without: range = 25 − 22 = 3°C.
(b) With: Σ = 177, mean ≈ 25.3°C. Without: Σ = 139, mean ≈ 23.2°C.
(c) Probably exclude if the report describes typical weather — but explicitly flag the heatwave as an anomaly. For an annual climate report, include it but note that it skews the range and mean.
1.4 — Class quiz
(a) Outlier = 2 (isolated far below the cluster 14–18).
(b) With: range = 18 − 2 = 16. Without: range = 18 − 14 = 4.
(c) Plausible reasons for scoring 2: student was unwell, misread instructions, or didn't have time to finish. The teacher might exclude it from class-performance analysis but should investigate the cause and offer the student a chance to re-sit.
1.5 — News headline
(a) A few extremely expensive sales (mansions or large blocks) inflate the mean but not the median.
(b) The headline uses the mean. It's misleading because most buyers will encounter prices around $850 000, not $1.6 million; the headline overstates affordability difficulty for typical buyers.
(c) Report the median ($850 000) in the headline, with the mean noted alongside and the few outlier sales explained separately.
2.1 — Explain your thinking (sample response)
The second analyst's correction matters because the range depends entirely on the max and min — missing a single high or low value changes the answer. A 12.0 s outlier shifts the range from 0.5 s to 1.8 s, more than tripling it; the conclusion changes from "highly consistent" to "moderately spread out". This shows how range can be misleading when even one outlier is present. A more reliable measure of spread is the interquartile range (IQR) — the range of the middle 50% of data — which ignores extreme values and gives a fairer picture of typical variability (it's covered in detail in Year 9).
Marking: 1 mark for noting range uses only two values; 1 mark for showing how one outlier shifts the conclusion; 1 mark for naming IQR as a more reliable spread measure; 1 mark for clear, full-sentence answer.