Comparing box-and-whisker graphs - CSSI

Compare distributions shown as box-and-whisker plots using the CSSI framework -- Centre (median, mean), Shape (left skew, right skew, symmetric/bell curve), Spread (IQR, range), and Interesting features (outliers, groups).

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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-INT-P-Y10-02
  • NZC26-P3-STA-INT-K-Y7-02

Resources

  • Alpha textbook: Box and Whisker plots, Ex 30.05-Ex 31.02, pg 517-542
  • Beta: Skills in Ex 30.01, pg 562
  • Beta: Skills in Ex 30.02, pg 570
  • CorbettMaths - Box PlotsQuestions PDF · Answers

Terminology

  • box-and-whisker graphs
  • centre
  • shape
  • spread
  • left skew / left tail
  • right skew / right tail
  • bell curve

Task goals

  • Apply the 75%-to-50% comparison rule when one distribution's quartile lies beyond the other distribution's median.
  • Recall what C, S, S, and I each stand for in the CSSI framework for comparing box-and-whisker plots.
  • Read the five-number summary (minimum, lower quartile, median, upper quartile, maximum) off a box-and-whisker plot.
  • Calculate and compare the interquartile range (IQR) and range as measures of spread.
  • Identify a distribution's shape (left skew, right skew, or symmetric) from the relative size of the box and whisker sections.
  • Identify outliers and other interesting or unusual features on a box-and-whisker plot.
  • Compare two or more distributions using centre, shape, spread, and interesting features together, and justify conclusions drawn from the comparison.

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

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Comparing box-and-whisker graphs - CSSI

Comparing box-and-whisker graphs - CSSI

Do

Making an informal inference in comparative situations about what might be happening in the population, based on visual considerations and using the 75%-to-50% comparison rule

Statement▸
Year 10 · Statistics · Interpretation of data
NZC26-P4-STA-INT-P-Y10-02

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