Mathematics • Year 7 • Unit 4 • Lesson 13
Misleading Graphs
Build fluency with the 4 main misleading techniques (truncated axis, 3D effects, inconsistent scales, cherry-picked time) and the STALC checklist (Scale, Title, Axes, Legend, Context). Data can be correct while the graph still lies.
1. I do, fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. A bar chart compares two phone brands' customer satisfaction: Brand X = 87%, Brand Y = 84%. The y-axis starts at 80%. Brand X's bar appears about four times taller than Brand Y's. Identify the misleading technique and explain how to fix it.
Step 1, Name the technique.
The y-axis starts at 80% (not 0%). This is a TRUNCATED AXIS.
Reason: only the top 7% (Brand X) vs 4% (Brand Y) above the baseline shows, so a 3% gap looks like a 4× difference.
Step 2, Calculate the real difference.
Real difference: 87% − 84% = 3 percentage points.
Percentage difference: 3 ÷ 84 × 100% ≈ 3.6%.
Reason: only ~3.6% better, small, not dramatic.
Step 3, Fix.
Redraw the chart with the y-axis starting at 0% (going up to 100%). Both bars will appear almost equal, an honest visual.
Answer: Misleading technique = truncated axis. Real difference = 3 percentage points (~3.6%). Fix: restart the y-axis at 0%.
2. We do, apply STALC to a graph
You are reviewing a graph titled "Sales SOAR as competitors FAIL". The y-axis starts at 80% and the axis intervals are 80, 85, 90, 100 (not equal). The y-axis has no unit label. The data covers only the best 3 months of the year. Fill in each blank with PASS or FAIL and a one-line reason. 5 marks
S, Scale: y-axis starts at 80% → _____________ . Intervals are unequal (80, 85, 90, 100) → _____________ .
T, Title: "Sales SOAR as competitors FAIL" is emotional / biased → _____________ .
A, Axes: y-axis has no unit label → _____________ .
L, Legend: assume a key exists → _____________ .
C, Context: only the best 3 months are shown → _____________ .
Overall verdict: _________________________________________________________
3. You do, independent practice
For each scenario, identify the misleading technique and (where asked) calculate the real difference. Quote specific values.
Foundation, spot the technique
3.1 A bar chart's y-axis starts at 95 instead of 0. Name the technique. 1 mark
3.2 A pie chart uses a 3D tilt so the front slice looks larger than the side slices. Name the technique. 1 mark
3.3 A graph of share prices shows only the 6 best months of the year, ignoring the other 6. Name the technique. 1 mark
3.4 A bar chart's y-axis intervals are: 0, 10, 20, 50, 100. State what is wrong with this scale. 1 mark
Standard, calculate and explain
3.5 A graph shows two companies' annual profits: Company A = $2,100,000 and Company B = $2,000,000. The y-axis starts at $1,950,000. (i) Calculate the real percentage difference. (ii) Explain why the bars look very different even though the values are close. 2 marks
3.6 Look at this title: "Test Scores PLUMMET After Bad Teaching!" State whether it is objective or biased, and rewrite it as a neutral title. 2 marks
Extension, fix a misleading graph
3.7 A line graph of a share price has the y-axis starting at $48. The price moves from $50 to $52 over 6 months, but the graph looks like a "dramatic surge". (i) Calculate the real percentage rise. (ii) Suggest TWO fixes to make the graph honest. 3 marks
3.8 Apply the full STALC checklist to a graph you have seen recently in the news, on social media, or in an ad. State a PASS/FAIL for each letter (S, T, A, L, C) with a one-line reason for each. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, STALC check (We do)
S: FAIL y-axis doesn't start at 0, and intervals (80, 85, 90, 100) are unequal.
T: FAIL"SOAR" and "FAIL" are emotional / biased.
A: FAIL y-axis has no unit label so the reader can't tell what's measured.
L: PASS a key is shown.
C: FAIL only the best 3 months are shown, not the full year (cherry-picked).
Verdict: 4 of 5 STALC checks fail, this graph is highly misleading.
3.1, Technique
Truncated axis (the y-axis does not start at zero).
3.2, Technique
3D effect (visual distortion, front slices look larger due to perspective).
3.3, Technique
Cherry-picking (showing only the best portion of the data, hiding the rest).
3.4, Unequal intervals
The scale intervals are not equal (the gap from 20 → 50 is 30, but it's drawn the same width as 0 → 10 which is 10). This is an inconsistent scale and distorts the visual shape of the data.
3.5, Company profits
(i) Real % difference = (2,100,000 − 2,000,000) ÷ 2,000,000 × 100% = 100,000 ÷ 2,000,000 × 100% = 5%.
(ii) Bars look very different because the y-axis starts at $1,950,000, so only the top $150,000–$200,000 of each bar is shown. A small 5% real difference fills most of the visible chart space, making it look much bigger than it really is.
3.6, Biased title
"Test Scores PLUMMET After Bad Teaching!" is biased ("plummet" is dramatic; "bad teaching" makes a claim without proof).
Neutral rewrite (sample): "Year 7 Test Scores, Term 1 vs Term 2".
3.7, Share price
(i) Real rise = (52 − 50) ÷ 50 × 100% = 2 ÷ 50 × 100% = 4%.
(ii) Fixes: (1) Start the y-axis at $0 (or use a clear zigzag break symbol to show the scale is not continuous). (2) Use equal intervals (e.g. $0, $10, $20, $30, $40, $50, $60). A neutral title and a clear x-axis label (Months Jan–Jun) also help.
3.8, STALC on a real graph (sample)
Sample: a news bar chart titled "Crime UP 200%!" comparing two months.
S: FAIL, y-axis starts at 100 incidents, not 0. Intervals look equal.
T: FAIL, "UP 200%" is dramatic; "Crime!" is loaded.
A: PASS, both axes labelled.
L: PASS, legend present.
C: FAIL, only 2 months shown; full-year context missing.
Marking: 1 for each of three or more PASS/FAIL judgements with a brief reason.