Mathematics • Year 10 • Unit 4 • Lesson 12
Scatter Plots and Correlation in the Real World
Apply Lesson 12's correlation framework to real Australian contexts: study habits, traffic, ice-cream sales and Olympic times. Then explain "correlation ≠ causation" by spotting confounding variables — the lesson's classic warning.
1. Word problems
For each scenario, describe the correlation (direction + strength + shape) using real numbers from the data and decide whether the relationship implies causation.
1.1 — Study minutes vs sleep hours. A Year 10 student tracks for one week:
(study min, sleep hr) = (30, 9.0), (60, 8.5), (90, 8.0), (120, 7.5), (150, 7.0), (180, 6.5), (240, 5.5).
(a) Plot the points on the axes below.
(b) Describe the correlation in one sentence (direction + strength + shape).
(c) Does extra study CAUSE less sleep? Suggest one other reason. 3 marks
|—————————————————————————————————————————————|
0 30 60 90 120 150 180 210 240
1.2 — Ice cream sales and drowning incidents (the classic). Across 12 months, ice cream sales (in $1000s) and drowning incidents per month at NSW beaches are strongly positively correlated. The Lesson 12 warning callout uses this exact example.
(a) Does buying ice cream cause people to drown?
(b) Name the third variable (the "confounding variable") that explains the link.
(c) State the lesson's two-word phrase that captures this idea. 3 marks
1.3 — Sydney commute times. Sydney commuters are surveyed: (distance from CBD in km, average morning commute in min):
(5, 25), (8, 30), (12, 38), (15, 45), (20, 55), (25, 65), (30, 80).
(a) Describe the correlation (direction + strength + shape) with numerical evidence — quote two points to support your claim.
(b) Is this evidence enough to claim that living further from the CBD CAUSES longer commutes? Justify in one sentence. 3 marks
1.4 — Olympic 100 m sprint times. The gold medal winning time (s) for the men's Olympic 100 m sprint has trended downward over decades:
(year, time) = (1980, 10.25), (1988, 9.92), (2000, 9.87), (2008, 9.69), (2016, 9.81), (2024, 9.79).
(a) Describe the correlation in one sentence.
(b) Why might the trend NOT continue strongly into 2040? (Lesson 12 misconception card hint: linear trends don't always continue forever.) 3 marks
1.5 — Confounding variables. For each correlation below, name a plausible confounding variable that could explain the link without one variable causing the other:
(a) Children with bigger feet score higher on reading tests.
(b) Towns with more churches have higher crime rates.
(c) Daily coffee sales and daily umbrella sales are positively correlated. 3 marks
2. Explain your thinking
This question is about communication, not just classification. Use full sentences. 4 marks
2.1 A news headline reads: "Study shows students who eat breakfast score 12% higher in exams — eat your breakfast!" Using Lesson 12's "correlation ≠ causation" idea, write a four-sentence reply that (i) identifies the correlation in the claim, (ii) explains why a positive correlation does NOT prove causation, (iii) names ONE plausible confounding variable, and (iv) finishes with one rule of thumb to help a Year 10 student avoid the trap.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Study min vs sleep hr
(a) Plot shows seven points trending downward from (30, 9.0) to (240, 5.5).
(b) Strong negative linear correlation between study minutes and sleep hours.
(c) Not necessarily causation: the student might use phones late, have homework deadlines, or skip sleep for many reasons — extra study is one cause but not the only one.
1.2 — Ice cream and drowning
(a) No. Ice cream does not cause drowning.
(b) Confounding variable: hot weather (summer) — both ice cream sales and beach swimming rise in hot months.
(c) "Correlation ≠ causation" (or "correlation does not imply causation").
1.3 — Sydney commute
(a) Strong positive linear correlation. Evidence: (5, 25) and (30, 80) — as distance increases 6-fold, commute time roughly triples.
(b) Not directly: distance is a major contributor, but the relationship is driven by traffic density, transport mode and route quality — these are causal mechanisms, distance is a proxy.
1.4 — Olympic 100 m
(a) Negative correlation: times have decreased over the years, though points (2016 and 2024) sit slightly above the 2008 record, so the trend is moderate not perfectly linear.
(b) Physical limits: human sprint times approach a biological floor. Lesson 12 misconception: a trend may not continue forever — the rate of improvement slows.
1.5 — Confounding variables
(a) Age — older children have bigger feet AND read better.
(b) Population size — bigger towns have more of everything (churches AND crime).
(c) Cold or rainy weather — people buy more hot coffee AND umbrellas on cold/wet days.
2.1 — Explain your thinking (sample)
The headline reports a positive correlation between eating breakfast and exam scores, not a cause-and-effect relationship. Lesson 12 warns that correlation does not imply causation — two variables can rise together without one causing the other. A plausible confounding variable is family routine or income: students from organised, well-resourced households often eat breakfast AND have more study support and quieter homes. The rule of thumb: before claiming "X causes Y", ask whether there is a third variable Z that explains both.
Marking: 1 mark for identifying the correlation, 1 for stating correlation ≠ causation, 1 for a plausible confounding variable, 1 for a clear rule of thumb.