Comparison across groups using suitable common-scale displays; Handling outliers, shape, centre and spread; Categorical proportions and modal category; Evidence-based conjectures and limitations
Example 1
Two groups have the same median but IQRs 4 and 9. Which is supported?
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Answer: The middle half of the second group is more spread out
- A larger IQR means greater spread in the middle 50%; it does not determine the median or all other features.
Example 2
A very large new outlier is added to a small dataset. Which centre measure is usually more resistant?
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Answer: Median
- The median depends on ordering and is less sensitive to an extreme magnitude than the arithmetic mean.
Example 3
Group A has mean 2 from 8 observations; group B has mean 5 from 4 observations. Find the combined mean.
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Answer: 3
- Use a weighted mean: total sum divided by total count, not the unweighted mean of group means.