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MathidiaMathematics Academy
Statistics and data
Lesson 65 of 75
Review

Compare distributions

Objective. Compare data sets using averages, spread and context.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Comparing distributions means using averages (mean, median or mode) alongside measures of spread (range or interquartile range) to judge how two data sets differ, rather than relying on a single number. A higher average shows one set generally scored higher, while a smaller spread shows more consistent results with less variation. Always state both an average comparison and a spread comparison, linked back to the context of the data. Example: if class A has mean 65 and range 10, while class B has mean 60 and range 30, class A scored higher on average and was more consistent.

Worked example

Team A has a mean score of 24 and a range of 4. Team B has a mean score of 20 and a range of 12. Compare the distributions of the two teams' scores.

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Bar chart of the values 24, 4, 20, 12
  1. 1Compare the means: Team A's mean of 24 is higher than Team B's mean of 20.
  2. 2Compare the ranges: Team A's range of 4 is smaller than Team B's range of 12.
  3. 3A smaller range shows more consistent scores with less variation.
  4. 4Team A scored higher on average and was more consistent than Team B.

Answer: Team A scored higher on average and was more consistent

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Common mistake. Pupils often compare only the averages and ignore the spread, missing that one group could be far less consistent despite a similar mean; always comment on both average and spread together.

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