Problem

Add \(10\) to \({8,9,10,11,12}\). Using median-of-halves quartiles, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and interpret the effect of repeating the central value.

Source distribution display: Add10 to data {8,9,10,11,12}. Using median-of-halves quartiles, compute mean, median, range, IQR before/after and interpret the central addition. No requested comparison or interpretation is annotated.

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before=(mean10,median10,range4,IQR3); after=(mean10,median10,range4,IQR2); changes=(mean0,median0,range0,IQR -1); interpretation=central repeated value leaves center/range unchanged and slightly tightens middle50%

before=(mean10,median10,range4,IQR3); after=(mean10,median10,range4,IQR2); changes=(mean0,median0,range +4,IQR +4); interpretation=central repetition is treated as making spread much larger

before=(mean10,median10,range4,IQR3); after=(mean10,median10,range4,IQR2); changes=(mean +4,median +4,range0,IQR −1); interpretation=adding central10 is treated as changing center greatly

before=(mean10,median10,range4,IQR3); after=(mean10,median10,range4,IQR2); changes=(mean0,median0,range −4,IQR −1); interpretation=range is treated as decreasing because the new value balances data

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Add \(10\) to \({8,9,10,11,12}\). Using median-of-halves quartiles, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and interpret the effect of repeating the central value.

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