Problem

Compare the variability of group A, with \(IQR~5\) and \(\text{range}~12\), and group B, with \(IQR~8\) and \(\text{range}~20\). Use both measures to justify the comparison.

Paired data displays or interval graphics on a shared scale without the requested comparison conclusion.

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What this problem is really about

Variability is about how widely values are spread, so larger spread measures point toward greater variability. Compare the groups on the same measure first, and use both the middle-half spread and the full-span spread as independent evidence before forming one conclusion.

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Group B has more variability because both its IQR and its range are larger.

Group A has more variability because the smaller IQR means its data are spread out more consistently.

Group A has more variability because 12 and 5 together are less balanced than 20 and 8 together.

The two groups have the same variability because each group is described by the same two measures, IQR and range.

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Compare the variability of group A, with \(IQR~5\) and \(\text{range}~12\), and group B, with \(IQR~8\) and \(\text{range}~20\). Use both measures to justify the comparison.

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