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Sample variance bessel correction · case 04

Population normalization biases the sample variance.

Member previewVariant 4 · 3 implementations · 4 checks per implementation

Case contract

Integer finite observations and equal lengths for paired samples. Counts and weights are nonnegative. Rational results use reduced Fraction strings. Empty or undefined statistics return None where shown. Sample variance bessel correction. Exact operational definition: str(statistics.variance([Fraction(v) for v in values])) if len(values)>1 else None

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Statistical estimators results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: ([1, 2, 3],)	`"2/3"`	`"1"`	Failed

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