Sample Standard Deviation Unbiased Proof
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Sample Standard Deviation Unbiased Proof. A more formal way to clarify the situation is to say that s (or the sample standard deviation) is an unbiased estimator of s , the population standard . @nrh's answer to this question gives a nice, simple proof of the biasedness of the sample standard deviation.
You might be thinking about how how the sample standard deviation tends to be lower than the population standard deviation on average.
The sample mean is an unbiased estimator of the population mean : However note that s is not . To see this, note that s is . S2=∑ni=1(xi−ˉx)2n−1 is the statistic that is always an unbiased estimator of the desired population parameter σ2.
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