Comparing distributions

Objective. Write contextual conclusions using centre and spread.

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Learn: the key idea

Comparing distributions means writing a conclusion that references both an average (centre) and a spread measure together with context, rather than listing numbers in isolation. State which group has the higher or lower centre (mean or median) and which has the larger or smaller spread (range or interquartile range), then explain what this means practically. For example, 'Class A had a higher median score but a larger interquartile range, so its results were higher on average but less consistent.' Always link each statistic back to the real-world context being compared.

Worked example

Team A has median 15 and IQR 4; Team B has median 12 and IQR 9. Write a comparison of these distributions regarding typical score and consistency.

1 $Compare medians: Team A (15) is higher than Team B (12)$
2 $Compare IQRs: Team A (4) is smaller than Team B (9)$
3 $Team A scores higher on average and more consistently$
4 $Team B scores lower on average and less consistently$

Answer: Team A scores higher on average and more consistently than Team B

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Common mistake. Students often state only that 'the median is bigger' without any spread comparison or context; a full statistical comparison always needs both centre and spread referenced together.

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