Problem

Determine whether range or \(IQR\) better reports typical spread while resisting \(\text{one}\) extreme high outlier. State the spread measure, how it matches the goal and condition, and the relevant statistical property.

Source statistical display: The goal is to report typical spread while resisting one extreme high outlier. Choose range or IQR. No requested analysis or conclusion is annotated.

Big Picture

What this problem is really about

Start with the reporting purpose: full endpoint-to-endpoint spread and typical middle spread answer different questions. Range directly uses both extremes, so an outlier can dominate it; IQR measures the middle half and is resistant when the goal is to describe ordinary variation despite an isolated extreme.

Answer choices

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Preview only

selected spread = IQR; match = typical middle spread with high outlier; property = IQR uses middle 50% and is resistant to the extreme

selected spread = range; match = resistance to an extreme is ignored; property = spread is treated as needing to change with every extreme

selected spread = range; match = typical spread with a high outlier; property = including the outlier is treated as representing typical spread

selected spread = IQR; match = typical middle spread with a high outlier; property = range and IQR are treated as equally affected by extremes

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Determine whether range or \(IQR\) better reports typical spread while resisting \(\text{one}\) extreme high outlier. State the spread measure, how it matches the goal and condition, and the relevant statistical property.

What this problem is really about

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