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 1.75 times as tall as Brand Y's because the displayed heights are 7 and 4 percentage points. 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 7 percentage points (Brand X) and 4 percentage points (Brand Y) above the baseline are shown. Their displayed-height ratio is 7 ÷ 4 = 1.75, while the actual values have ratio 87 ÷ 84 ≈ 1.04.
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: the $2,100,000 bar is $150,000 above the baseline, while the $2,000,000 bar is $50,000 above it. The displayed-height ratio is 3 ÷ 1 = 3, even though the actual profits differ by only 5%.
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.