Comparing Distributions
How do I compare averages of two distributions?
- Choose the appropriate average (mode, median or mean)
- The mean includes all the data
- The median is not affected by extreme values
- The mode can be used for non-numerical data
- Consider whether it is better for the average to be bigger or smaller
- If you are comparing time to complete a puzzle - the smaller average the better
- If you are comparing test scores - the bigger the average the better
- Give numerical values for the average and explicitly compare
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E.g.The mean for dogs is 17 kg which is bigger than the mean for cats which is 13 kg
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- Give your comparison in context
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E.g.The mean for dogs is bigger which suggests that dogs are heavier than cats on average
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How do I compare ranges of two distributions?
- Choose the appropriate range (range or interquartile range)
- The range is affected by extreme values
- The interquartile range focuses on the middle 50%
- Consider whether it is better for the range to be bigger or smaller
- A smaller range implies consistency
- A bigger range implies more spread
- Give numerical values for the range and explicitly compare
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E.g.The interquartile range for dogs is 6 kg which is bigger than the interquartile range for cats which is 4 kg
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- Give your comparison in context
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E.g.The interquartile range for cats is smaller which suggests that the weights of cats are more consistent and similar
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Worked Example
Julie collects data on the distances travelled by snails and slugs over the duration of ten minutes. She records a summary of her findings as shown in the table below.
| Median | Interquartile range | |
| Snails | 7.1 cm | 3.1 cm |
| Slugs | 9.7 cm | 4.5 cm |
Compare the distances travelled by snails and slugs over the duration of ten minutes.
Slugs have the higher median (9.7 > 7.1) which suggests that on average slugs move further than snails. Snails have the lower interquartile range (3.1 < 4.5) which suggests that there is less variation in the distances travelled by snails.
