Problem

For equal-width histogram bins \([0,10)\), \([10,20)\), \([20,30)\), and \([30,40)\), group A has counts \(2,~6,~5,~1\) and group B has counts \(1,~5,~5,~4\). Calculate the middle-bin and high-bin proportions, locate each median bin, compare the distributions, and state the limit on recovering exact medians.

Source distribution display: Equal-width histogram bins [0,10),[10,20),[20,30),[30,40) have A counts2,6,5,1 and B counts1,5,5,4. No requested comparison or interpretation is annotated.

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middle proportions=A11/14≈0.786,B10/15≈0.667; high-bin proportions=A1/14≈0.071,B4/15≈0.267; median-bin ordering=A median in [10,20), B median in [20,30), so B's median is higher; conclusion=B also has more high-end mass/a longer high tail; exact median values cannot be recovered from bins

middle proportions=A11/14≈0.786,B10/15≈0.667; high-bin proportions=A1/14≈0.071,B4/15≈0.267; median-bin ordering=A[10,20),B[20,30); conclusion=histograms identical because middle bins overlap; exact median values cannot be recovered

middle proportions=A11/14≈0.786,B10/15≈0.667; high-bin proportions=A1/14≈0.071,B4/15≈0.267; median-bin ordering=A[10,20),B[20,30); conclusion=no comparison possible; bin ordering and tail evidence are ignored

middle proportions=A11/14≈0.786,B10/15≈0.667; high-bin proportions=A1/14≈0.071,B4/15≈0.267; median-bin ordering=A[10,20),B[20,30); conclusion=B must have a larger exact median; exact median values are incorrectly claimed known

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