Mathematics • Year 7 • Unit 4 • Lesson 13
Misleading Graphs — Mixed Challenge
Bring together all four misleading techniques, the STALC checklist, percentage-difference calculations, and graph fixes. Spot a flawed "honest" judgement, then design a fully honest version of a misleading graph.
1. Mixed problems
Each question uses a different misleading technique or STALC check. Justify briefly. 2 marks each
1.1 A bar chart shows two bars with the y-axis starting at 90. State the technique and one consequence for the reader.
1.2 Calculate the real percentage difference between $1,050 and $1,000.
1.3 A pie chart of school activities is drawn in 3D and tilted forward. Sport (20%) is at the front and looks bigger than Music (35%) at the back. State the technique and the fix.
1.4 Match each STALC letter to its check: S, T, A, L, C. Write each pair as "Letter → check it does".
1.5 A graph's x-axis tick marks go: 2018, 2019, 2020, 2022, 2024 (skipping 2021 and 2023). State which STALC letter fails and why.
1.6 A truthful business owner wants to show monthly profit but the actual values are very close ($998, $1000, $1002, $1001, $999). How should they make a clear line graph WITHOUT being misleading? Suggest one safe technique and one warning sign for the reader.
2. Find the mistake
A Year 7 student wrote the following analysis of a bar chart. Exactly one statement contains a serious error in logic. 3 marks
The graph: Bar A = 86%, Bar B = 84%. The y-axis runs from 80% to 90%. Bar A's bar is 60 pixels tall; Bar B's bar is 40 pixels tall.
Statement 1: The two real values are very close (only 2 percentage points apart).
Statement 2: The bars look about 1.5× different because the y-axis is truncated (starts at 80%).
Statement 3: This graph is honest because the underlying numbers (86% and 84%) are correct.
Statement 4: To fix the graph, the y-axis should start at 0%.
(a) Which statement contains the mistake?
(b) Explain in one or two sentences why that statement is wrong.
(c) Write the corrected statement.
Stuck? Revisit lesson § "Spot the Trap" — "data correct" is NOT the same as "graph honest".3. Open-ended challenge — design a misleading vs honest pair
This question has many correct answers. Show your work clearly. 4 marks
3.1 Two stores compete on customer satisfaction. Store A scored 80%; Store B scored 78%. You are asked to draw TWO bar charts:
- a misleading version that makes Store A look dramatically better than Store B, and
- an honest version that accurately shows the small real difference.
For each version, describe in words: (i) where the y-axis starts and ends, (ii) any 3D/colour tricks used (in the misleading version) or avoided (in the honest version), (iii) the title you'd give it, and (iv) one sentence on what impression the reader will get.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Truncated axis
Technique: truncated axis (y-axis starts at 90, not 0). Consequence: small real differences look much larger than they actually are, exaggerating the gap between bars.
1.2 — Percentage difference
% difference = (1050 − 1000) ÷ 1000 × 100% = 50 ÷ 1000 × 100% = 5%.
1.3 — 3D pie chart
Technique: 3D visual distortion (front slices appear larger). Fix: redraw as a flat 2D pie chart with clear percentage labels.
1.4 — STALC matching
S → check the SCALE starts at zero and intervals are equal.
T → check the TITLE is objective, not biased or emotional.
A → check both AXES are labelled with units.
L → check a LEGEND/key is provided.
C → check the CONTEXT (full time period, not cherry-picked).
1.5 — Skipping years
S (Scale) fails — the x-axis intervals are not equal (it skips 2021 and 2023), so a steady year-on-year change would look uneven, distorting any trend the graph shows.
1.6 — Honest small differences
Safe technique: use a line graph with a zigzag break symbol on the y-axis so the reader knows the scale doesn't start from 0. Warning sign: the zigzag (also called a "broken axis" or "axis break") tells the reader the y-axis has been truncated honestly.
2 — Find the mistake
(a) The mistake is in Statement 3.
(b) Correct data does NOT mean the graph is honest. The numbers 86% and 84% are correct, but starting the y-axis at 80% (truncated) makes a 2-point difference look 1.5× bigger on screen, which IS misleading.
(c) Corrected: This graph is misleading even though the underlying numbers are correct, because the truncated y-axis (starts at 80%) visually exaggerates the small real difference.
3 — Two graphs (sample design)
Misleading version: y-axis from 76% to 82%; 3D bars; Store A coloured bright red, Store B faded grey; title "Store A LEADS the Market!". Reader will think Store A is far better than Store B even though the gap is only 2 percentage points.
Honest version: y-axis from 0% to 100%; flat 2D bars; both stores the same neutral colour; title "Customer Satisfaction: Store A vs Store B". Reader will see two nearly identical bars and correctly conclude the difference is small (2 points).
Marking: 1 for misleading axis choice + 1 for biased title; 1 for honest axis 0–100 + 1 for neutral title.