Calculating averages and range

Calculate the mean, median, and mode (the three measures of centre) and the range of a dataset, work backwards from a given mean to find a missing value, and judge which measure of centre best represents a dataset (especially when an outlier is present).

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Alpha textbook: Measures of centre, Ex 30.02 – Ex 30.05, pg 519-526
  • CorbettMaths on mean, median, mode, and rangeQuestions PDF · Answers
  • Dr Austin Maths - Averages and Range Revision Practice GridQuestions PDF · Answers
  • Beta: Skills in Ex 30.01, pg 562

Terminology

  • Mean
  • Median
  • Mode
  • Range
  • Variation

Task goals

  • Calculate the mean of a dataset (sum divided by count), including cases where the mean is not a whole number.
  • Calculate the median of a dataset with an odd or even count of values (for an even count, average the middle two after sorting).
  • Find the mode of a dataset, including recognising when a dataset has no mode.
  • Calculate the range of a dataset as maximum minus minimum, and describe what it represents (the spread/variation within the data).
  • Work backwards from a given mean and a known number of values (with some values missing) to find a missing value.
  • Judge which measure of centre (mean, median, or mode) best represents a dataset, especially explaining why the median or mode can be more representative than the mean when an outlier is present.

Key skills

  • Mean
  • Median
  • Mode
  • Range
  • Spread
  • Measures of centre

Quick stats

  • 0 total questions
  • 3 difficulty levels
  • Answers included
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