Problem

In \({16,17,18,19,20,100}\), replace \(100\) with \(20\). Using median-of-halves quartiles, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and interpret the change in shape.

Source distribution display: In data {16,17,18,19,20,100}, replace100 with20. Using median-of-halves quartiles, compute mean, median, range, IQR before/after and interpret skew change. No requested comparison or interpretation is annotated.

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What this problem is really about

Replacing an extreme value lets you see which statistics depend on distance from the center and which depend mainly on ordered middle positions. Build parallel before-and-after lists, recompute every measure under the same quartile rule, and use signed changes to connect numerical sensitivity with the disappearance of a long tail.

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before=(mean=95/3≈31.67,median18.5,range84,IQR3); after=(mean=55/3≈18.33,median18.5,range4,IQR3); changes=(mean0,median0,range −80,IQR0); shape=mean is treated as unchanged because20 is above center

before=(mean=95/3≈31.67,median18.5,range84,IQR3); after=(mean=55/3≈18.33,median18.5,range4,IQR3); changes=(mean −40/3,median0,range +80,IQR0); shape=right tail removed while range is treated as increasing

before=(mean=95/3≈31.67,median18.5,range84,IQR3); after=(mean=55/3≈18.33,median18.5,range4,IQR3); changes=(mean -40/3,median0,range -80,IQR0); shape=extreme right tail removed, so much less right-skewed

before=(mean=95/3≈31.67,median18.5,range84,IQR3); after=(mean=55/3≈18.33,median18.5,range4,IQR3); changes=(mean −40/3,median0,range −80,IQR0); shape=replacing100 with20 is treated as creating left skew

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In \({16,17,18,19,20,100}\), replace \(100\) with \(20\). Using median-of-halves quartiles, calculate the before-and-after mean, median, range, and \(IQR\); report each signed change; and interpret the change in shape.

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