Problem

Determine whether range or \(IQR\) better reports typical middle spread for a box plot with \(\text{one}\) extreme high value beyond a long upper whisker. State the spread measure, how it matches the goal and condition, and the relevant statistical property.

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selected spread = IQR; match = long upper whisker; property = long whiskers are treated as proving even spread

selected spread = range; match = a long upper whisker with an extreme value; property = outliers are treated as barely affecting max-min

selected spread = IQR; match = middle spread with extreme high value; property = Q3-Q1 excludes the extreme endpoint

selected spread = range; match = typical middle spread with an extreme high value; property = a full box plot is treated as requiring range

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