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Section 16.3 · Statistics and probability

Choosing the right average

Choose and explain which of the mode, median and mean is most appropriate for a given context, and recognise the effect of an outlier.

6 teaching slides 48 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

outlierA value far away from all the others.
appropriateThe right choice for this particular context.
distortPull a statistic away from what is typical.
typicalWhat most of the data looks like.
consistentVarying little; having a small range.
categorical dataData that is words or labels, not numbers.

3 · Summary of the sectionrevise from this

  • All three of mode, median and mean are averages. They choose the representative value differently.
  • Mode: use it for categories and for “which is most popular”. It is the only one that works for words.
  • Median: use it when there is an outlier or the data is lopsided — house prices, salaries.
  • Mean: use it when the values are close together with no extremes. It uses every value.
  • An outlier moves the mean a long way and the median hardly at all.
  • Do not silently delete an outlier. Investigate it, and say what you decided.
  • Always quote a range alongside an average — the average alone says nothing about spread.
  • A smaller range means more consistent.
  • In an examination the reason earns the mark, not the name of the average.
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4 · Practice48 questions, easiest first

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16.2 The mean
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16.4 Reading charts and graphs