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MathidiaMathematics Academy
Statistics and distributions
Lesson 63 of 75
Standard practice

Box plots

Objective. Construct and compare distributions using five-number summaries.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Box plots summarise a distribution using its five-number summary: minimum, lower quartile, median, upper quartile and maximum, drawn as a box with whiskers. The box spans from the lower to upper quartile with a line at the median, while whiskers extend to the minimum and maximum values. For example, data with minimum 2, Q1 = 5, median 8, Q3 = 11 and maximum 15 produces a box from 5 to 11 with a line at 8. Comparing two box plots side by side lets you judge differences in both centre (median) and spread (interquartile range).

Worked example

A box plot has minimum 4, lower quartile 9, median 14, upper quartile 20 and maximum 27. Find the interquartile range shown by this box plot.

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Bar chart of the values 4, 9, 14, 20, 27
  1. 1Interquartile range = upper quartile − lower quartile
  2. 2Upper quartile = 20, lower quartile = 9
  3. 3IQR = 20 − 9
  4. 4IQR = 11

Answer: 11

Concept mastery

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Practice

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Common mistake. Students often compare only the medians of two box plots and ignore the spread; a full comparison needs both the median (centre) and the interquartile range (consistency) stated in context.

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