[Phys-l] sample variance versus population variance

[John Denker <jsd@av8n.com>]

On 10/09/2006 05:25 PM, Krishna Chowdary wrote:

> > I don't think the standard deviation of the mean (aka "standard error")
> > is what is needed here.  The st. dev. of the mean tells you how well you
> > know the mean value, but that isn't what is important.  You want the
> > effect of the variation of the individual trials, which is related to
> > the plain old standard deviation.
>
> Now that you point this out, I'm not sure what to do.


Are we talking about the sample variance versus population variance?
If so, the fix is simple:  replace N by N-1 in the normalization.
That allows you to convert the sample variance into an unbiased predictor
of the population variance.

  http://mathworld.wolfram.com/SampleVariance.html

But perhaps I have misunderstood the question.  The generally-used notation
is so messed up that all sorts of inconsistencies can arise.