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Box Plots

FoundationHigherAQAEdexcel

Revise Box Plots for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. A box plot displays the minimum, lower quartile, median, upper quartile and maximum of a data set.

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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

A box plot displays five key values, giving a clear visual summary of a distribution and making comparison between two data sets straightforward.

The five values are the minimum, lower quartile, median, upper quartile and maximum. The box spans from the lower to the upper quartile, with a line inside marking the median. Whiskers extend from the box to the minimum and maximum.

The box therefore shows the interquartile range, and its width shows the spread of the middle 50 per cent. Two box plots drawn on the same scale allow direct comparison of both average and spread. Box plots do not show individual values or the frequency of any particular value.

Revision notes

The five-figure summary

Minimum, lower quartile, median, upper quartile, maximum.

The box spans \(Q_1\) to \(Q_3\) with the median marked inside. Whiskers extend from the box edges to the minimum and maximum values.

What the box shows

The width of the box is the interquartile range, showing the spread of the middle 50 per cent.

The position of the median line within the box indicates skewness — a median nearer the left edge suggests positive skew.

Comparing box plots

Two box plots on the same scale allow direct comparison.

Compare an average, usually the median, and a measure of spread, usually the interquartile range. Both are needed for full marks. Box plots do not show individual values or frequencies.

Key points

  • A box plot shows five key values.
  • The box spans the lower to upper quartile.
  • The median is marked inside the box.
  • Whiskers reach the minimum and maximum.
  • The box width is the interquartile range.
  • Box plots do not show individual values.

Worked examples

Example 1

A box plot has \(Q_1 = 15\) and \(Q_3 = 27\). Work out the width of the box. [2 marks]

Working

The box spans from \(Q_1\) to \(Q_3\), so the width is \(27 - 15\)identify what the box width represents
\(= 12\), which is the interquartile rangework out the value

Example 2

List the five values shown on a box plot. [2 marks]

Working

Minimum, lower quartile and mediangive the first three
Upper quartile and maximumgive the remaining two

Example 3

Explain why box plots are useful for comparing two data sets. [2 marks]

Working

Both plots can be drawn on the same scale, one above the otherstate the property
so the medians and interquartile ranges can be compared directly by eyeexplain the benefit

Common mistakes

  • Drawing whiskers to the quartiles.

    Whiskers extend to the minimum and maximum.

  • Comparing only the median.

    Comparison questions want both an average and a measure of spread.

  • Saying a box plot shows frequency.

    It shows five summary values only, not how many values occur.

  • Forgetting to mark the median.

    The line inside the box is essential.

Exam tips

  • Learn the five-figure summary in order.
  • Compare both median and interquartile range.
  • Draw both plots on the same scale.
  • Remember the box width is the IQR.

Key terms

Box plot
A diagram showing a five-figure summary.
Five-figure summary
Minimum, quartiles, median and maximum.
Whisker
A line extending to the minimum or maximum.
Interquartile range
The width of the box.

Related topics

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