🚀 go-pugleaf

In article <seX2yRq00Uh785H2EB@andrew.cmu.edu> dr3u+@andrew.cmu.edu (Daniel Read) writes:
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>Can someone explain why calculating the Standard Deviation (SD),
>for small samples, with (n-1) in the denominator is better than
>doing so with (n) in the denominator?  I'm sure that there's
>a perfectly good reason for doing so.  But we, lowly engineers
>aren't usually told the reason.  Thanks now, for your response later.;-)

This is done in only in the case of the _sample_ standard deviation. The
reason for this is that the _sample_ mean is used in the formula, rather
than the population mean. Using a denominator of (n-1) results in the sample
_variance_ being unbiased -- the expected value of the sample variance will
be the population variance. (Unfortunately, the sample standard deviation
will be slightly biased. It is difficult to come up with an unbiased sample
standard deviation; I imagine that the square root make the results
dependent on the underlying distribution. So the goal is to make the sample
_variance_ unbiased.)

For a proof of this, check any introductory text on mathematical statistics.
If you'd like to try it yourself, take the expected value of the sample
variance. Expand the (x - xbar)**2 term inside.