Recognising Misleading Graphs (Higher)
Recognising misleading graphs is the skill of spotting chart features that create a false or exaggerated impression of the data, such as a vertical axis that does not start at zero, inconsistent scales, missing labels, or images scaled by area rather than by a fixed size. Explaining why a specific feature distorts the true pattern, using real numbers from the graph, is assessed on both tiers of GCSE Statistics.
Before you start
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Method
- Check the vertical axis: does it start at zero? A truncated axis makes small real differences look much bigger than they are.
- Check the axis scale: is it consistent, with equal gaps for equal jumps in value? An uneven scale distorts how far apart bars or points appear.
- Check for missing information: are the axes labelled with units, is there a title, and is a key or scale given? Missing labels can hide an unfavourable interpretation.
- Check for visual exaggeration: are bars drawn in 3D, or are images scaled by area or volume instead of a fixed size? These make differences look bigger than the true ratio of the values.
- Check the sample size and any selective use of data: is the full data set shown, or has an unrepresentative or short time period been chosen to support a particular story?
- State clearly which specific feature is misleading and explain, using actual numbers from the graph where possible, how it distorts the reader's impression.
Worked example
A company's bar chart shows profit, in thousands of pounds, for two years. The vertical axis runs from 40 to 50, not starting at 0. The bar for 2023 reaches 42, and the bar for 2024 reaches 48. Explain how this graph could mislead a reader, and describe the true percentage increase in profit.
- Identify the misleading feature: the vertical axis runs from 40 to 50 rather than starting at 0, so it is truncated.
- Explain the visual effect: measured from the axis start of 40, the 2023 bar has a visual height of 42 - 40 = 2 units and the 2024 bar has a visual height of 48 - 40 = 8 units, a ratio of 4 to 1.
- Calculate the true percentage increase: (48 - 42)/42 x 100 = 6/42 x 100 = 14.3% (1 decimal place).
- Compare the two impressions: the true increase is about 14.3%, far smaller than the roughly four-times-taller impression the truncated axis creates.
- Final answer: the truncated y-axis exaggerates the apparent increase in profit; profit actually rose by about 14.3%, not by the much larger amount the graph visually suggests.
Practice questions
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Q1Why is starting a bar chart's vertical axis at a value other than zero considered misleading?Show answer
Answer: It exaggerates the visual difference between bars, making small real differences look much larger than they are
Q2A pictogram uses house-shaped images to represent numbers of houses built, where a bigger house image represents a bigger number. Explain why scaling the image by area rather than using a repeated fixed-size symbol can mislead.Show answer
Answer: If both the width and height of the image are scaled up, its area increases faster than the actual increase in value (area grows with the square of the scale factor), making the increase look larger than it really is
Q3A line graph comparing two companies' sales uses a different scale on the left and right vertical axes, without making this clear. Why is this misleading?Show answer
Answer: It can make two data sets that behave very differently appear to track closely together, when their actual values or rates of change are not really comparable
Q4A bar chart's vertical axis is truncated to run from 200 to 260. Bar A reaches 210 and Bar B reaches 250. Calculate the ratio of the bars' heights as drawn, and the true percentage difference between the values.Show answer
Answer: Drawn ratio is 5 to 1 (heights of 10 and 50 from the axis start of 200); true percentage difference = (250-210)/210 x 100 = 19.0% (1 d.p.)
Q5A newspaper graph shows a crime rate rising sharply, using only the last 3 months of data out of 5 years of records, with a vertical axis truncated from 30 to 36 crimes per 1000 people. Give two separate reasons this graph could be misleading.Show answer
Answer: Using only the last 3 months ignores the wider 5-year trend and may not represent the true long-term pattern; and the truncated axis (30 to 36) exaggerates how large the rise looks compared to the true scale of change
Q6A company reports that sales doubled using a bar chart where the 2023 bar is drawn 2 cm tall and the 2024 bar is drawn 4 cm tall, but the axis (which starts at 0) is labelled only at the top: 2023 = 150,000 pounds and 2024 = 210,000 pounds. Explain the inconsistency and calculate the true percentage increase.Show answer
Answer: True increase is 40% ((210,000-150,000)/150,000 x 100), not a doubling; since the axis starts at 0, a bar twice as tall should mean double the value (300,000), but 210,000 is not double 150,000, so the bars have not been drawn to scale and exaggerate the rise
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A bar chart comparing two towns' populations has a vertical axis that starts at 8000 instead of 0. State one way this could mislead a reader, and suggest how to fix it.
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A pie chart claims to show market share for four companies, but the four sectors' angles do not add up to 360 degrees and no percentages or values are labelled. (a) State two ways this pie chart could mislead a reader. (b) Explain how the chart should be corrected.
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A fitness company advertises that members lose weight fast using a line graph of average member weight, in kg, over 12 weeks. The vertical axis runs from 78 to 80 kg, and only weeks 1, 6 and 12 are plotted: 80 kg (week 1), 79.4 kg (week 6), 78.8 kg (week 12). (a) Describe two features of this graph that could mislead a reader. (b) Calculate the true percentage decrease in weight from week 1 to week 12. (c) Explain how the graph makes this change look more dramatic than it is.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the recognising misleading graphs (higher) worksheet pack - 25 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 16 of GCSE Statistics Higher Workbook 1, the whole course as one free printable PDF.
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