Problem

In \({3,40,41,42,43,44}\), correct \(3\) to \(40\). 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 {3,40,41,42,43,44}, correct3 to40. Using median-of-halves quartiles, compute mean, median, range, IQR before/after and interpret tail change. No requested comparison or interpretation is annotated.

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before=(mean35.5,median41.5,range41,IQR3); after=(mean=125/3≈41.67,median41.5,range4,IQR3); changes=(mean −37/6,median0,range −37,IQR0); shape=low outlier correction is treated as decreasing mean and creating right skew

before=(mean35.5,median41.5,range41,IQR3); after=(mean=125/3≈41.67,median41.5,range4,IQR3); changes=(mean +37/6,median0,range +37,IQR0); shape=more left-skewed while range is treated as increasing

before=(mean35.5,median41.5,range41,IQR3); after=(mean=125/3≈41.67,median41.5,range4,IQR3); changes=(mean +37/6,median0,range −37,IQR0); shape=statistics are treated as changing little because40 is near42

before=(mean35.5,median41.5,range41,IQR3); after=(mean=125/3≈41.67,median41.5,range4,IQR3); changes=(mean +37/6≈+6.17,median0,range -37,IQR0); shape=low outlier removed, so much less left-skewed

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In \({3,40,41,42,43,44}\), correct \(3\) to \(40\). 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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