Problem

Data set A has box-plot summary minimum \(5\), \(Q_{1}\) \(8\), median \(10\), \(Q_{3}\) \(12\), maximum \(15\). Data set B has box-plot summary minimum \(10\), \(Q_{1}\) \(13\), median \(14\), \(Q_{3}\) \(16\), maximum \(20\). Compare their centers and spreads.

Paired data displays or interval graphics on a shared scale without the requested comparison conclusion.

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What this problem is really about

Compare like features rather than judging the plots by overall position or a single endpoint. Medians compare center, box widths compare middle-half spread, and maximum-minus-minimum spans compare full spread; calculate each pair separately because the data set with the higher center need not have the larger spread.

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Data set B has the higher center because its maximum is larger, data set B also has the larger spread because its values go up to 20, and its range is greater than data set A's.

Data set A has the higher center because its minimum is lower, and although data set B has a smaller IQR, it has a larger range because 20 is greater than 15.

Data set B has the higher center because its median is 14 instead of 10, data set A has the slightly larger IQR because 12-8 is 4 while 16-13 is 3, and both data sets have the same range of 10.

The two data sets have the same center because their box plots are about the same width, but data set B has the slightly larger IQR and a larger range.

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Data set A has box-plot summary minimum \(5\), \(Q_{1}\) \(8\), median \(10\), \(Q_{3}\) \(12\), maximum \(15\). Data set B has box-plot summary minimum \(10\), \(Q_{1}\) \(13\), median \(14\), \(Q_{3}\) \(16\), maximum \(20\). Compare their centers and spreads.

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