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Box Plots

HigherHigher tier onlyAQAEdexcelOCR

Practise box plots with this free Higher GCSE Maths worksheet from Virtus Academy. You'll work through drawing and comparing box plots, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. A box plot shows the minimum, quartiles, median and maximum.

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

This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A box plot summarises a distribution using five figures: the minimum, lower quartile, median, upper quartile and maximum.

The box spans the interquartile range, with a line inside marking the median. Whiskers extend from the box to the minimum and maximum values.

Box plots are ideal for comparison, because two can be drawn on the same scale and read at a glance. A comparison answer should mention both an average and a measure of spread, and interpret both in context.

Revision notes

The five-figure summary

A box plot needs the minimum, \(Q_1\), the median, \(Q_3\) and the maximum.

The box runs from \(Q_1\) to \(Q_3\), so its width is the interquartile range. The whiskers reach the extremes.

Drawing accurately

Use the same scale as any box plot you are comparing with, and draw against a labelled axis.

The median line must be positioned accurately within the box, since its position shows whether the data is skewed.

Comparing distributions

Compare a measure of average, usually the median, and a measure of spread, usually the interquartile range.

A higher median means typically larger values; a smaller interquartile range means more consistency. Both points must be put in context to earn full marks.

Key points

  • A box plot uses five figures.
  • The box spans \(Q_1\) to \(Q_3\).
  • The box width is the interquartile range.
  • A line inside the box marks the median.
  • Whiskers reach the minimum and maximum.
  • Compare an average and a spread in context.

Worked examples

Example 1

A box plot has \(Q_1 = 24\) and \(Q_3 = 41\). Find the interquartile range.

Working

\[41 - 24\]the box width is the interquartile range
\[= 17\]state the interquartile range

Example 2

A box plot shows minimum \(12\) and maximum \(58\). Find the range.

Working

\[58 - 12\]maximum minus minimum
\[= 46\]state the range

Example 3

Group A has median \(30\) and IQR \(8\); Group B has median \(25\) and IQR \(15\). Compare them.

Working

\[30 > 25\]Group A has the higher median, so typically larger values
\[8 < 15\]Group A has the smaller IQR, so it is more consistent

Common mistakes

  • Comparing only the medians.

    A full comparison needs an average and a measure of spread.

  • Drawing box plots on different scales.

    They must share a scale to be compared.

  • Confusing the range with the interquartile range.

    The whiskers show the range; the box shows the IQR.

  • Not putting the comparison in context.

    Say what the difference means for the data, not just which number is larger.

Exam tips

  • Write out the five-figure summary before drawing.
  • Use the same scale when comparing two box plots.
  • Always compare both an average and a spread.
  • Interpret both comparisons in the words of the question.

Key terms

Box plot
A diagram showing the five-figure summary.
Whisker
A line extending to the minimum or maximum.
Five-figure summary
Minimum, Q1, median, Q3 and maximum.
Skew
Asymmetry, shown by the median's position in the box.

Related topics

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