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.

Current NZC (2007)
  • S5-1
New NZC (2026)
  • NZC26-P4-STA-DKD-P-Y10-02
  • NZC26-P3-STA-DKD-K-Y7-02
  • NZC26-P3-STA-DKD-K-Y7-03
  • NZC26-P3-STA-DKD-P-Y7-02
  • NZC26-P3-STA-DKD-P-Y7-03
  • NZC26-P3-STA-INT-P-Y7-01

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.

Where this fits

What leads into this objective, and where it goes next.

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Calculating averages and range

Calculating averages and range

Do

Reasoning why a mean or median would be a better measure of central tendency for a given statistical question

Statement▸
Year 10 · Statistics · Developing knowledge from data
NZC26-P4-STA-DKD-P-Y10-02

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