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Understanding how averages are calculated – KS4 maths lesson plan

Key Stage



Years 10-11


Understanding how different kinds of averages are calculated and behave is an important skill, says Colin Foster…

In this lesson, students tackle a statistical puzzle which forces them to adjust some numbers to create certain values of the mean, mode, median and range in various small datasets.

There are multiple simultaneous constraints, which makes this a challenging problem, and there are opportunities for students to create simple proofs of impossibility.

Why teach this?

This lesson reviews mean, median, mode and range by offering a statistical puzzle that illuminates the connections between them.

Key curriculum links

  • Make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples
  • Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

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