Comparing Distributions

Spec reference: Statistics
Key idea: Compare two data sets using averages and measures of spread.

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What to compare

When comparing two distributions, always comment on both:

1. Average (mean, median or mode) - which is higher/lower
2. Spread (range or IQR) - which is more/less consistent

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Using box plots to compare

A box plot (box and whisker diagram) shows:

• Minimum value
• Lower quartile (LQ)
• Median
• Upper quartile (UQ)
• Maximum value

$$\text{IQR}=\text{UQ}-\text{LQ}$$

A smaller IQR means the data is more consistent.

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Writing comparison statements

Always include:

• A comparison of the averages (e.g. "Group A has a higher median of 65 compared to Group B's median of 58")
• A comparison of the spread (e.g. "Group A is more consistent with a smaller IQR of 12 compared to 20")
• A contextual conclusion

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Back-to-back stem and leaf

Used to compare two small data sets. The leaves for one set go left, the other right.

Read the left-hand data set from right to left.

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Test Yourself

Question 1 of 5

Group A median 65, Group B median 58. Who performed better?