[R] Different value between R variance and definition of variance

[Daniel Nordlund]

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf
> Of Tine
> Sent: Wednesday, November 28, 2007 12:57 AM
> To: r-help at r-project.org
> Subject: [R] Different value between R variance and definition of variance
> 
> Hi!
> 
> Let us define random variable:
>  > x = seq(0,1,length=100)
> 
> If we calculate variance following definition E[(x-E(x))^2] we get:
>  > mean( (x - mean(x))^2 ) # == mean(x^2) - mean(x)^2
> 0.08501684
> 
> And if we use internal R function var:
>  > var(x)
> 0.08587559
> 
> Can anyone tells me why the difference?
> 

I haven't seen a response, so I will chime in.  R calculates an unbiased estimate of the population variance from which your x is assumed to be a simple random sample of size n (in your case n=100).  See any basic book on statistics.  So, using your formula, R "in effect" calculates

     mean((x-mean(x)^2) * n/(n-1)

Hope this is helpful,

Dan 

Daniel Nordlund
Bothell, WA USA