Problem

Add \(30\) to \({8,9,10,11,12}\). Using the median-of-halves convention, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and compare the measures' resistance to the outlier.

Source statistical display: Add 30 to {8,9,10,11,12}. Using the median-of-halves convention, compute mean, median, range, and IQR before and after; identify each signed change and resistance comparison. No requested comparison or classification is annotated.

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What this problem is really about

An extreme new value does not affect every summary in the same way. Recompute each statistic from its definition, then use the size of each change to distinguish summaries that react strongly to distant values from summaries that mostly track the ordered middle of the data.

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before=(mean10, median10, range4, IQR3); after=(mean=40/3≈13.33, median10.5, range22, IQR3); changes=(mean +18, median +18, range +18, IQR +18); comparison=all measures are treated as equally sensitive

before=(mean10, median10, range4, IQR3); after=(mean=40/3≈13.33, median10.5, range22, IQR3); changes=(mean +10/3, median +0.5, range +18, IQR 0); comparison=median/IQR are more resistant than mean/range

before=(mean10, median10, range4, IQR3); after=(mean=40/3≈13.33, median10.5, range22, IQR3); changes=(mean −10/3, median +0.5, range +18, IQR 0); comparison=mean is treated as decreasing while range increases

before=(mean10, median10, range4, IQR3); after=(mean=40/3≈13.33, median30, range22, IQR3); changes=(mean +10/3, median +20, range +18, IQR 0); comparison=median is treated as becoming the added value

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Add \(30\) to \({8,9,10,11,12}\). Using the median-of-halves convention, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and compare the measures' resistance to the outlier.

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