Problem

Classify the histogram with equal-width nonoverlapping bins \([0,10)\), \([10,20)\), and \([20,30)\) and counts \(2,~5,~\text{and}~2\). Report its modality and modal bin, symmetry or skew, uniformity, gaps, and supporting count evidence.

Source statistical display: Which complete classification correctly describes equal-width nonoverlapping histogram bins [0,10),[10,20),[20,30) with counts 2,5,2? No requested comparison or classification is annotated.

Big Picture

What this problem is really about

For equal-width histogram bins, the ordered bar heights carry the shape information. Find the tallest interval, compare bars that sit equally far from it, and check whether all heights are similar or any interval is empty; those separate checks establish modality, balance, uniformity, and gaps.

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modality=all bins tied; symmetry=roughly symmetric; uniformity=uniform; gaps=none; evidence=counts2,5,2 are treated as equal

modality=unimodal, modal bin=[10,20) count5; symmetry=roughly symmetric; uniformity=not uniform; gaps=none; evidence=outer bins have equal count2 around central peak5

modality=unimodal, modal bin=[10,20) count5; skew=left-skewed; uniformity=not uniform; gaps=none; evidence=outer equal counts2 are treated as a left tail

modality=unimodal, modal bin=[10,20) count5; skew=right-skewed; uniformity=not uniform; gaps=none; evidence=outer equal counts2 are treated as a right tail

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Classify the histogram with equal-width nonoverlapping bins \([0,10)\), \([10,20)\), and \([20,30)\) and counts \(2,~5,~\text{and}~2\). Report its modality and modal bin, symmetry or skew, uniformity, gaps, and supporting count evidence.

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