Problem

For test scores, class A has median \(82\) and \(IQR\) \(6\), while class B has median \(78\) and \(IQR\) \(14\). Calculate the center and spread differences, interpret their signs, and state the contextual conclusion.

Source statistical display: Test scores: class A median82,IQR6; class B median78,IQR14. No requested comparison or classification is annotated.

Big Picture

What this problem is really about

A complete comparison needs two parallel stories: one about typical performance and one about consistency. Compute both differences in the same group order, then remember that a positive center difference identifies the higher typical value while a smaller spread indicates greater consistency.

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median difference=+4 points, so B higher; IQR difference=6−14=−8 points, so B more consistent; conclusion=B typically scores higher and is more consistent

median difference=+4 points, so A has the higher typical score; IQR difference=6-14=-8 points, so A's middle50% is less spread/more consistent; conclusion=A typically scores higher and is more consistent

median difference=+4 points, so A lower; IQR difference=6−14=−8 points, so A is more consistent; conclusion=A typically scores lower but is more consistent

median difference=+4 points, so typical scores are the same because difference4 is ignored; IQR difference=6−14=−8 points, so A is more consistent; conclusion=same typical score with A more consistent

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For test scores, class A has median \(82\) and \(IQR\) \(6\), while class B has median \(78\) and \(IQR\) \(14\). Calculate the center and spread differences, interpret their signs, and state the contextual conclusion.

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