Problem

Compare the groups' variability using both \(IQR\) and range: group A has \(IQR~4\) and \(\text{range}~30\), while group B has \(IQR~10\) and \(\text{range}~18\). Identify the group with greater spread by each measure and explain the difference.

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Group A has more variability by both measures because its range is larger, so its data must also be more spread out in the middle.

Group B has more variability by both measures because its IQR is larger, so it must also be more spread out overall.

Group A has more total spread because its range is 30 instead of 18, but Group B has more middle-half spread because its IQR is 10 instead of 4.

The groups have the same variability because each group has one larger spread measure, so the differences cancel out.

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