Mathematics • Year 7 • Unit 4 • Lesson 12
Interpreting Graphs — Real World
Apply trend, peak, trough, cluster, gap and outlier to real graphs: Sydney temperatures, monthly rainfall, double bar charts, a class quiz dot plot, and a school-fundraising line graph.
1. Word problems
Each scenario gives you the data behind the graph. Quote specific values and units. Use the language: trend, peak, trough, cluster, gap, outlier.
1.1 — Sydney average temperatures. Average monthly maximum temperatures (°C): Jan 26, Feb 26, Mar 25, Apr 22, May 19, Jun 17, Jul 16, Aug 18, Sep 20, Oct 22, Nov 24, Dec 25.
Describe the peak, the trough, and the overall annual pattern in 2–3 sentences. Include values and months. 4 marks
1.2 — Quiz scores dot plot. Marks (out of 20) for 12 students: 18, 5, 14, 15, 16, 17, 13, 14, 15, 16, 19, 18.
(a) Identify the outlier and state its value.
(b) Identify the cluster (give the range of values it covers).
(c) In one sentence, explain what the outlier suggests about that student's performance. 3 marks
1.3 — School fundraising. Money raised each week ($) for 8 weeks: 200, 250, 220, 300, 320, 800, 310, 290.
(a) Identify the outlier and the week it occurred.
(b) Suggest one real-world reason the outlier might have occurred (e.g. a special event).
(c) Describe the overall trend if the outlier is removed. 3 marks
1.4 — Double bar chart. Term 1 and Term 2 averages for two schools.
School A: Term 1 = 68%, Term 2 = 74%.
School B: Term 1 = 72%, Term 2 = 70%.
(a) Describe each school's trend with the change in marks (e.g. "+6%").
(b) Which school had the higher average in Term 1, and which in Term 2?
(c) Suggest one real-world reason School A may have improved. 4 marks
1.5 — Daily rainfall. Rainfall (mm) over 10 days: 0, 0, 0, 0, 5, 12, 35, 0, 0, 0.
(a) Identify the cluster of days with no rain (state which days).
(b) Identify the peak rainfall and the day it occurred.
(c) Suggest in one sentence what this graph might be showing in real-world terms (e.g. one storm during a dry spell). 3 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A Year 7 student looks at a line graph of monthly ice cream sales AND monthly drowning incidents (both peak in summer) and says: "Eating more ice cream causes more drownings." Explain (i) why this conclusion is wrong, (ii) the term for the mistake the student is making (correlation vs causation), and (iii) what the real common cause of both trends is.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Sydney temperatures
Peak: 26 °C in January and February (summer in the Southern Hemisphere). Trough: 16 °C in July (winter). The overall pattern shows a clear seasonal cycle — temperatures fall from summer through autumn to a July low, then rise again into spring and back to a summer peak.
1.2 — Quiz scores dot plot
(a) Outlier: 5 (much lower than every other score).
(b) Cluster: between 13 and 19 (the other 11 students).
(c) The outlier suggests one student performed far below the rest of the class — possibly due to absence on the day of the quiz, illness, or needing extra support.
1.3 — School fundraising
(a) Outlier: $800 in week 6.
(b) Possible reasons include a one-off trivia night, a school disco, or a big cake-stall day.
(c) If the outlier is removed, the trend is a gentle increase from $200 to about $310 across the other 7 weeks — fundraising is slowly improving.
1.4 — Double bar chart
(a) School A: +6% (68 → 74). School B: −2% (72 → 70).
(b) Term 1: School B (72%) > School A (68%). Term 2: School A (74%) > School B (70%).
(c) School A may have improved because of better teaching interventions, more student effort, or extra tutoring — but the graph alone cannot prove the cause. (Use cautious language.)
1.5 — Daily rainfall
(a) Cluster of 0 mm days: days 1–4 and days 8–10.
(b) Peak: 35 mm on day 7.
(c) This graph likely shows a single storm event (around day 6–7) during an otherwise dry 10-day period.
2.1 — Explain your thinking (sample response)
(i) The conclusion is wrong because the graph only shows that ice-cream sales and drownings rise at the same time — it does not show that one causes the other. (ii) This mistake is called confusing correlation with causation. Just because two variables move together does not mean one causes the other. (iii) The real common cause is summer weather — hot weather makes people both buy more ice cream AND swim more often, which increases the number of drownings. Ice cream sales do not cause drowning; both are caused by the same underlying factor.
Marking: 1 for explaining the bad logic; 1 for naming correlation vs causation; 1 for identifying summer/heat as common cause; 1 for clear sentences.