Quartiles and box plots · Grade 8

In Grade 8 you learn: comparing distributions.

Averages tell you a typical value. Measures of spread tell you how much the data vary. Quartiles split ordered data into four equal parts. A box plot shows the minimum, quartiles, median and maximum at a glance.

Key facts

  • Range = maximum − minimum. One extreme value can change it a lot.
  • Q1 is the median of the lower half and Q3 is the median of the upper half. With an odd number of values, leave the median out of both halves.
  • Interquartile range IQR = Q3 − Q1: the spread of the middle 50%.
  • An outlier is more than 1.5 × IQR below Q1 or above Q3.
  • A box plot shows the minimum, Q1, median, Q3 and maximum on a scale.
  • To compare data sets, compare the medians (average) and the IQRs (consistency).

Worked examples

Example 1

Find the median and the interquartile range of 3, 5, 7, 8, 10, 12, 15.

Answer: Median 8, IQR 7

Example 2

The box plots show test marks for two classes. Compare them.

Answer: A scored higher on average; B was more consistent

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