Mathematics • Year 8 • Unit 4 • Lesson 13
Misleading Graphs in the Real World
Apply graph-critique skills to real-world contexts: political campaigns, product advertising, news headlines, social media stats, and climate reporting. Each problem demands both identification and a calculation.
1. Word problems
Each problem uses a misleading-graph technique from Lesson 13. Show calculation working.
1.1 — Political ad. A campaign ad shows a bar chart of "Crimes per year" with bars labelled 2 401, 2 405, 2 408, 2 412 over 4 years. The y-axis starts at 2 400. The headline reads: "Crime up sharply!"
(a) Identify the misleading technique.
(b) Calculate the actual percentage change from year 1 to year 4 (1 d.p.).
(c) Is the headline justified? Justify in one sentence. 3 marks
1.2 — Cereal box pictograph. A cereal company claims that fibre content has doubled. They double the height AND width of a wheat stalk icon to show this. The original icon was 1 cm × 1 cm.
(a) What are the new icon's dimensions?
(b) Calculate the new icon's area.
(c) By what factor has the icon area grown? Why is this misleading? 3 marks
1.3 — News headline. A news article shows: "Average home prices DOUBLE in 5 years!" with a bar chart. Actual values: 2018 = $620k, 2023 = $740k. The chart's y-axis starts at $600k.
(a) Identify the misleading techniques used (there are two).
(b) Calculate the actual percentage change to 1 d.p.
(c) Rewrite a more accurate headline using the real percentage. 3 marks
1.4 — Social media stats. An influencer posts a graph titled "My followers exploded this month!" The line shows follower counts: Week 1 = 10 200, Week 2 = 10 220, Week 3 = 10 240, Week 4 = 10 260. The y-axis runs from 10 195 to 10 270.
(a) Identify the technique.
(b) Calculate the actual percentage growth across the month.
(c) Suggest how a more honest graph could be drawn. 3 marks
1.5 — Climate cherry-pick. A blog publishes a graph of Sydney's average July temperatures for the past 5 years (2019-2023), where the values happen to dip slightly. They claim: "Sydney is cooling — climate change is a hoax." They ignore the previous 50 years of data, which shows steady warming.
(a) Identify the misleading technique.
(b) Explain in one sentence why looking at only 5 years is a problem for a climate claim.
(c) What is the ONE question you would ask the blog writer to expose the trick? 3 marks
2. Explain your thinking
This question is about critique, not just numbers. Use full sentences. 4 marks
2.1 Your friend forwards you a chart from a website with the title "Brand X is 4 times more popular than Brand Y!" The bars are labelled X = 52% and Y = 48%, but the y-axis runs from 45% to 55%, making X's bar appear 4 times taller than Y's. Explain (i) what misleading technique is being used, (ii) what the actual ratio of popularity is (calculated), (iii) why "4 times more popular" is a deceptive claim, and (iv) one concrete rule you will apply to ANY chart you see in the future. Use the term truncated axis in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Political crime ad
(a) Truncated y-axis (starts at 2 400, not 0).
(b) % change = (2 412 − 2 401) ÷ 2 401 × 100 = 11 ÷ 2 401 × 100 ≈ 0.5%.
(c) The headline is not justified — a 0.5% rise over 4 years is essentially flat, not "sharply up". The truncated axis creates a false visual impression.
1.2 — Cereal pictograph
(a) New dimensions: 2 cm × 2 cm.
(b) New area = 2 × 2 = 4 cm² (original was 1 cm²).
(c) Area grew by a factor of 4, not 2. Our eyes read AREA, so the icon visually suggests fibre quadrupled, when it actually only doubled. To represent doubling honestly, use TWO icons of the original size — not one icon of doubled dimensions.
1.3 — Home prices headline
(a) Truncated y-axis (starts at $600k) AND misleading verbal claim ("double" is wrong).
(b) % change = (740 − 620) ÷ 620 × 100 = 120 ÷ 620 × 100 ≈ 19.4%.
(c) Honest headline: "Average home prices up around 19% over 5 years."
1.4 — Influencer stats
(a) Truncated y-axis (range 10 195-10 270, just 75 units wide).
(b) % change = (10 260 − 10 200) ÷ 10 200 × 100 = 60 ÷ 10 200 × 100 ≈ 0.6%.
(c) Redraw with the y-axis starting at 0, or use a percentage-change chart. Either way, gaining 60 followers in a month for an account with 10 000+ is essentially no growth — the graph misrepresents this.
1.5 — Climate cherry-pick
(a) Cherry-picking — choosing only 5 years that suit the argument while ignoring the broader trend.
(b) Climate is a long-term trend. 5 years is far too short to overturn 50 years of warming data; short-term fluctuations are normal.
(c) "Why have you excluded the previous 50 years of data — what does the graph look like from 1973 to 2023?"
2.1 — Explain your thinking (sample response)
The chart uses a truncated axis (running 45% to 55% instead of 0% to 100%) to inflate a 4-percentage-point difference into a visual that looks like a 4× gap. The actual ratio of popularity is 52 ÷ 48 ≈ 1.08, so Brand X is only about 8% more popular than Brand Y, not 4 times more popular. The claim "4 times more popular" is doubly deceptive because (i) the bar-height ratio (~4×) is a visual artefact of the truncated axis, and (ii) the words confuse "X is 4 percentage points ahead" with "X is 4 times as big". My rule going forward: always check where the y-axis starts before reading any bar chart, and if it isn't 0, mentally rescale the bars.
Marking: 1 mark for naming truncated axis; 1 mark for the correct ratio (1.08); 1 mark for explaining the rhetorical trick ("4 times" vs "4 percentage points"); 1 mark for a concrete personal rule.