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Bounds represent the points with which data cannot exceed, such as minima or maxima.

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

So, my first question is: Have the tightest bounds been described in the literature, and if so, where? … In case this question cannot be answered positively, I have a follow-up question: Are the bounds I derive below the tightest ones? (To start perhaps: Are they valid?) …
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