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a sequence of objects or individuals collected from a larger (possibly infinite) population or process.

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Tightest bounds on sample variance given sample size, mean, minimum, and maximum

For real-valued samples (possibly known to lie in some interval, but without further constraints on them), I am interested in the tightest possible bound on the sample variance $\sigma^2$, given the sample … size $n$, sample mean $\mu$, sample minimum $m$, and sample maximum $M$. …
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