Problem

Box A has \(Q_{1}=10\), median \(15\), \(Q_{3}=20\), and a low outlier at \(2\); box B has \(Q_{1}=11\), median \(15\), \(Q_{3}=19\), and \(\text{no}~\text{flagged}~\text{outlier}\). Calculate the IQRs and box intersection, compare the typical middle values, interpret the outlier evidence, and identify unsupported claims.

Source distribution display: Box A has Q1=10,median15,Q3=20 and low outlier2; Box B has Q1=11,median15,Q3=19 and no flagged outlier. No requested comparison or interpretation is annotated.

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medians=A15,B15; box intersection=[11,19] length8; IQRs=A10,B8; supported=no comparison possible because boxes overlap; unsupported=equal medians and A's distinct outlier support conclusions

medians=A15,B15; box intersection=[11,19] length8; IQRs=A10,B8; typical middle values substantially overlap with equal medians; outlier conclusion=A alone has one flagged unusually low value at2; unsupported=distributions are identical or B is universally larger

medians=A15,B15; box intersection=[11,19] length8; IQRs=A10,B8; supported=B is larger in every value because A has low outlier2; unsupported=one outlier proves universal ordering

medians=A15,B15; box intersection=[11,19] length8; IQRs=A10,B8; supported=distributions are identical because medians and boxes overlap; unsupported=outlier2 is a distribution difference

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