Mathematics • Year 7 • Unit 4 • Lesson 13

Misleading Graphs — Real World

Apply STALC to graphs from news, ads, politics and social media. Calculate the real percentage difference. Decide whether each graph is honest, slightly misleading, or fully deceptive.

Apply · Real-World Maths

1. Word problems

Each scenario describes a real-world misleading graph. Identify the technique(s), calculate the real difference, and explain the fix.

1.1 — Election night. A news bar chart shows Candidate A: 2,100,000 votes; Candidate B: 2,000,000 votes. The y-axis starts at 1,950,000.

(a) Calculate the real percentage gap between the two candidates.
(b) Name the misleading technique used.
(c) How should the chart be redrawn to be honest? 4 marks

Stuck on (a)? % difference = (bigger − smaller) ÷ smaller × 100%.

1.2 — Unemployment rate. A media graph shows unemployment "DOUBLED!" with two bars: 5.1% in Q1 vs 5.2% in Q2. The y-axis starts at 5.0%.

(a) Calculate the actual percentage-point change.
(b) Is the headline "DOUBLED!" justified? Why or why not?
(c) Suggest a neutral title. 3 marks

Stuck on (b)? "Doubled" means 2× the original. Did 5.1% become 10.2%?

1.3 — Pie chart in an ad. A 3D pie chart shows market share. Slice A is at the front and looks the largest. The percentage labels say: A = 30%, B = 35%, C = 35%.

(a) Which slice is actually the largest?
(b) Why does Slice A appear largest even though it's not?
(c) Recommend a fix. 3 marks

Stuck on (b)? 3D pie charts distort perspective — front slices look bigger due to the tilt.

1.4 — Climate cherry-pick. A graph claims "Global temperatures are FALLING!" by showing data only from 1998 to 2008, ignoring all data before and after.

(a) Name the misleading technique.
(b) Explain in one sentence why this is dishonest.
(c) What time period would give an honest picture? 3 marks

Stuck on (c)? An honest climate graph shows many decades — say 1880 to now.

1.5 — School comparison. A school ad shows a bar chart titled "Our Year 7 Students Achieve TWICE the Average!". The y-axis starts at 60%. The school's average is 75% and the state average is 73%.

(a) Calculate the real difference (in percentage points).
(b) Apply the STALC checklist: identify ONE failure each for S, T and C. 4 marks

Stuck? "TWICE" claims a 100% difference. The real difference is 2 percentage points.

2. Explain your thinking

Communication matters. Use full sentences. 4 marks

2.1 A friend says: "If the numbers in a graph are correct, then the graph itself must be honest." Explain (i) why this is wrong with reference to the truncated-axis technique, (ii) one other technique a graph can use to mislead even with correct data, and (iii) the most important first check you should do on any bar chart.

Stuck? Revisit lesson § "Spot the Trap" — correct data does NOT mean honest graph.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

1.1 — Election night

(a) Real gap = (2,100,000 − 2,000,000) ÷ 2,000,000 × 100% = 100,000 ÷ 2,000,000 × 100% = 5%.
(b) Truncated axis (y-axis starts at 1.95M, not 0).
(c) Fix: restart the y-axis at 0. Both bars will appear nearly equal, accurately showing the small 5% gap rather than a fake landslide.

1.2 — Unemployment rate

(a) Actual change = 5.2% − 5.1% = 0.1 percentage points.
(b) NO. "Doubled" would mean 5.1% became 10.2%. The real change is tiny (0.1 percentage points). The headline is dishonest.
(c) Sample neutral title: "Unemployment rate: Q1 vs Q2".

1.3 — 3D pie chart

(a) Slices B and C are tied for largest at 35% each. Slice A (30%) is the SMALLEST.
(b) The 3D tilt makes the front slice (A) appear larger than it really is due to perspective distortion.
(c) Use a flat (2D) pie chart with percentage labels — readers can then judge slice sizes correctly.

1.4 — Climate cherry-pick

(a) Cherry-picking (selecting only the data period that supports the argument).
(b) Cherry-picking just 10 years (1998–2008) hides the long-term warming trend visible across many decades.
(c) An honest graph would show data from at least the late 1800s to the present (e.g. 1880–2024).

1.5 — School comparison

(a) Real difference = 75% − 73% = 2 percentage points (about 2.7% relative). NOT "twice" — that would be a 100% difference.
(b) STALC failures:
S — y-axis starts at 60% (truncated), not 0.
T — "TWICE the Average" is dramatically wrong / biased.
C — only the school's own students are compared (cherry-picked context); no error bars or sample size given.
Marking: 1 for correct difference; 1 each for S, T, C reasoning.

2.1 — Explain your thinking (sample response)

(i) Correct numbers do not make an honest graph. A truncated axis (starting at a value above zero) can make a tiny real difference look like a huge gap — the data is right but the visual is misleading. (ii) Other techniques include 3D effects (distorting slice sizes in pies), inconsistent scale intervals (e.g., 0, 10, 20, 50, 100) and cherry-picking the time period to hide the inconvenient part of the data. (iii) The most important first check on any bar chart is to look at where the y-axis starts — if it doesn't start at zero, be suspicious and calculate the real percentage difference yourself.

Marking: 1 for correct/honest distinction; 1 for explaining truncated axis; 1 for another technique; 1 for stating "axis start" as the first check.