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Misleading Graphs

FoundationHigherAQAEdexcel

Understand Misleading Graphs for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Graphs can mislead through truncated axes, unequal scales or distorted areas.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Graphs can be drawn in ways that mislead the reader, and identifying these faults is examined directly.

The most common fault is a vertical axis that does not start at zero, which exaggerates differences between bars or the steepness of a trend. A broken or non-linear scale has the same effect, as do unequal class widths on a histogram drawn using frequency rather than frequency density.

Other faults include unequal bar widths, missing axis labels or key, three-dimensional effects that distort apparent size, and pie charts compared without regard to their totals. When asked to criticise a graph, name the specific fault and explain the false impression it creates — both halves are needed for full marks.

Revision notes

Axis faults

A vertical axis not starting at zero exaggerates differences between bars and the steepness of trends.

A broken axis, or a scale with unequal or non-linear intervals, has the same effect. Check the axis before reading any graph.

Bar and area faults

Unequal bar widths make some bars look more significant than they are.

Three-dimensional effects distort apparent size. On a histogram, using frequency as the height with unequal class widths exaggerates the wider classes.

Answering criticism questions

Name the specific fault, then explain the false impression it creates.

Saying a graph is 'misleading' without both parts loses marks. For example: the axis starts at 40, so the difference between the bars appears far larger than it actually is.

Key points

  • A vertical axis not starting at zero exaggerates differences.
  • Broken or non-linear scales mislead.
  • Unequal bar widths distort importance.
  • Three-dimensional effects distort apparent size.
  • Missing labels or keys prevent interpretation.
  • Name the fault and explain the false impression.

Worked examples

Example 1

A bar chart's vertical axis starts at 50. Explain why this is misleading. [2 marks]

Working

All the bars are shortened by the same amount, so the differences between them appear proportionally much largerstate the effect
giving the false impression that the categories differ far more than they actually doexplain the false impression

Example 2

Give two features that make a graph misleading. [2 marks]

Working

A vertical axis that does not start at zerogive the first
Unequal bar widths, or a three-dimensional effect that distorts apparent sizegive the second

Example 3

A histogram with unequal class widths uses frequency as the bar height. Explain why this is misleading. [2 marks]

Working

The wider classes produce bars of much greater area than narrow classes with the same frequencystate the effect
so they appear more significant than they are, and frequency density should be used insteadexplain the false impression and the fix

Common mistakes

  • Saying a graph is misleading without naming the fault.

    Identify the specific feature causing the problem.

  • Naming the fault without explaining its effect.

    Both halves are needed for full marks.

  • Missing an axis that does not start at zero.

    Check the axis origin on every graph.

  • Ignoring three-dimensional distortion.

    It exaggerates the size of nearer or larger elements.

Exam tips

  • Always check whether the axis starts at zero.
  • Name the fault AND explain the false impression.
  • Learn several distinct misleading features.
  • Check class widths on any histogram.

Key terms

Misleading graph
A graph drawn so as to give a false impression.
Broken axis
An axis with a section removed, exaggerating differences.
Non-linear scale
A scale whose intervals are not equally spaced.
Distortion
Making something appear larger or smaller than it is.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.