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From: "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Variance?
Date: Thu, 15 May 2008 22:33:02 +0000 (UTC)
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"saneman" <asd@ad.com> wrote in message <g0iag5$m5r$1@news.net.uni-
c.dk>...
> How is it possible to use these functions on the data without supplying 
> information about the probabilities? 
---------
  The 'mean', 'var', and 'std' functions all make the assumption that all values 
they receive in vectors are the result of some stationary random process.  They 
apply equal weighting to each data point and simply produce what is termed 
"sample" means and variances.  The probabilities involved in the random 
process can be of any statistical kind.  Of course these samples means and 
variances are only estimations for the true underlying probabilistic means and 
variances, but they are the best that can be obtained from a finite sample.  If you 
have two sample results of 2 and 4, the best you can do is to estimate the mean 
as 3, but for such a small sample, this is an unreliable estimate.  If you have a 
billion values and their average is 3, that is much more likely to be close to the 
correct answer.

Roger Stafford