Sheet № 245 · Foundation + Higher · AQA · Edexcel · OCR
Misleading Graphs and Data –
Misleading graphs and data questions appear on GCSE Maths papers at Foundation and Higher tier. They test your ability to critically evaluate how data is presented — a skill that is increasingly important in everyday life as well as in exams. AQA, Edexcel and OCR all include questions where you must spot why a graph or statistical claim i
§Key definitions
Question:
A company's bar chart shows sales of £102 000 in January and £108 000 in February. The y-axis starts at £100 000. Explain why this graph is misleading.
Answer:
The graph is misleading because the vertical axis does not start at zero. This exaggerates the difference between the two months, making it look as if sales tripled when they actually increased by less than 6%.
Q1 (Foundation):
A bar chart comparing two shops' profits has a y-axis starting at £40 000. Shop A made £42 000 and Shop B made £46 000. Explain why the chart could be misleading.
Q2 (Foundation):
A survey of 10 people is used to claim "80% of people prefer brand X." Give one reason why this claim may be unreliable.
Q3 (Higher):
A graph shows temperature increasing from 14.8°C to 15.2°C over 50 years. The y-axis runs from 14.5°C to 15.5°C. A headline says "temperatures rocket." Evaluate this claim using a calculation.
§Formulas to memorise
Percentage change = (change ÷ original) × 100
Truncated vertical axis — starting the y-axis at a value other than zero makes small differences look dramatically large.
Inconsistent scale — unequal intervals on an axis distort the shape of the data.
Misleading pictograms — scaling both width and height of an image doubles makes it appear four times as large (area effect).
Cherry-picked data — showing only a selected time period or subset that supports a particular conclusion.
3D effects — adding unnecessary depth to bars or pie slices distorts their apparent size.
Missing labels or units — without clear labels, the reader cannot interpret the data properly.
Check the axes — does the vertical axis start at zero? Are the intervals equal and consistent?
Check the scale — are the gaps between values on each axis evenly spaced?
Check the labels — are both axes clearly labelled with units? Is there a title?
Worked example
A company's bar chart shows sales of £102 000 in January and £108 000 in February. The y-axis starts at £100 000. Explain why this graph is misleading.
Working:
⚠ Common mistakes
- ✗Not explaining the effect. It is not enough to say "the axis does not start at zero" — you must explain why this is misleading (e.g. "it makes the difference look bigger than it really is").
- ✗Confusing misleading with wrong. The data can be accurate while the presentation is misleading — the issue is the visual impression, not the numbers.
- ✗Ignoring the question context. Always refer to the specific data in the question, not generic criticisms.
- ✗Not suggesting a fix. Examiners often want you to say how the graph should be corrected — for example, "start the y-axis at zero" or "use equal intervals on the scale."
- ✗Overlooking sample size. A statistic based on a tiny sample is unreliable — always question whether the data set is large enough to support the claim.
✦ Exam tips
- →Look for truncated axes first — this is the most commonly tested trick on GCSE papers.
- →If asked to "criticise" or "comment on" a graph, make at least one specific point about what is misleading and explain the impact on the reader.
- →Calculate the actual percentage change to support your argument — this shows strong mathematical reasoning and earns full marks.
- →When discussing pictograms, mention the area effect explicitly: doubling both dimensions quadruples the visual area.
- →Always suggest a correction — for example, "the y-axis should start at zero" or "the sample should be larger and randomly selected."