Measures of centre/spread

Read a dot plot to find the mode (tallest stack), median (middle dot), and range (first-to-last occupied value), and calculate the mean, for a data set -- including working backwards from a given mean to find a missing value, and judging which measure of centre best represents a data set that contains an outlier. Discourage the word "average" in favour of naming the specific measure. Distinct from the existing lo-calculating-averages-and-range, which is entirely computation-only (a list of raw numbers, no diagram anywhere); this LO's task decks embed a live \PicStatisticsDotPlot diagram in every card, so students read three of the four measures directly off a genuine display before calculating the mean.

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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-Y9-02
  • NZC26-P4-STA-DKD-P-Y9-03
  • NZC26-P4-STA-DKD-P-Y10-02
  • NZC26-P3-STA-VIS-K-Y7-05
  • NZC26-P3-STA-VIS-K-Y7-06
  • NZC26-P3-STA-VIS-P-Y7-02
  • NZC26-P3-STA-INT-P-Y7-04

Resources

Terminology

  • Mean (Average)
  • Median (Middle)
  • Mode (Most Common)
  • Range
  • Spread

Task goals

  • Read the mode (tallest stack) and range (first-to-last occupied value) directly off a dot plot.
  • Read the median off a dot plot, correctly handling both an odd count (single middle dot) and an even count (mean of the two middle dots).
  • Calculate the mean of a data set shown on a dot plot.
  • Work backwards from a target mean to find a missing data value.
  • Judge whether the mean or the median better represents a "typical" value when a data set contains an outlier, and justify the choice.
  • Explain why the range is far more sensitive to a single outlier than the median is, and recognise "average" as ambiguous shorthand for a specific measure of centre.

Where this fits

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

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Measures of centre/spread

Measures of centre/spread

Do

Calculating the five-point-summary for numerical data: the minimum value; the value of quartile 1, or Q1; the value of the median or quartile 2, or Q2; the value of quartile 3, or Q3; the maximum value

Statement▸
Year 9 · Statistics · Developing knowledge from data
NZC26-P4-STA-DKD-P-Y9-02
Do

Calculating the interquartile range as IQR = Q3 − Q1

Statement▸
Year 9 · Statistics · Developing knowledge from data
NZC26-P4-STA-DKD-P-Y9-03

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