Quartiles

Order a dataset and split it into quarters to find the lower quartile (Q1), the median (Q2), and the upper quartile (Q3), calculate the interquartile range (IQR = Q3 minus Q1) as a measure of spread, and read the five-number summary (minimum, Q1, median, Q3, maximum) from a box-and-whisker graph.

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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

Resources

  • Alpha textbook: Box and Whisker plots, Ex 30.08, pg 532-533
  • CorbettMaths on quartilesQuestions PDF · Answers
  • Beta: Skills in Ex 30.01, pg 562

Terminology

  • Minimum
  • Lower Quartile / Q1
  • Median / Q2
  • Upper Quartile / Q3
  • Maximum
  • Interquartile range
  • Box-and-whisker graph
  • Dot plot

Task goals

  • Sort a dataset and split it into quarters to locate Q1, the median (Q2), and Q3, using the exclusive method (excluding the overall median from each half when the count is odd).
  • Calculate the interquartile range (IQR = Q3 - Q1) and explain that it measures the spread of the middle 50% of the data.
  • Read the five-number summary (minimum, Q1, median, Q3, maximum) from a box-and-whisker graph, including comparing two or more box plots by their medians and IQRs.
  • Explain why the IQR is a more outlier-resistant measure of spread than the range.
  • Determine what fraction of a dataset lies above or below a given quartile (e.g. recognise that one quarter of the data lies below Q1).

Where this fits

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

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Quartiles

Quartiles

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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