Re: var(x) and std(x)

[Mike Miller]

On Tue, 12 Nov 2002, Anand V wrote:

>   I have a doubt regarding the implementation of variance function
> var(x) in octave.
[snip]

>    It gives variance after averaging over n-1 samples, rather than
> averaging over n samples. for example, if we calculate the variance of x
> = [1,2,3] , it returns the value 1, instead of 2/3..This is because it
> finds 2/2 and not 2/3..The same is the case with std(x) also.
> Is it an error or is there any explanation for that?


It is not an error.  Variances are computed as the sum of squared
deviations about the mean divided by some term.  One might divide by n,
but this produces an estimator that is biased, so it is more common to
divide by n-1 because use of n-1 produces a variance estimator that is
unbiased.  Octave and MATLAB both use n-1 in var and std.  It's a good
choice, I think.

So, Octave uses all n values, but it divides the sum of squares by n-1.

Mike

-- 
Michael B. Miller, Ph.D.
Assistant Professor
Division of Epidemiology
University of Minnesota
http://taxa.epi.umn.edu/~mbmiller/



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