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Re: Puzzled by the "Variance"

• To: mathgroup at smc.vnet.net
• Subject: [mg86513] Re: Puzzled by the "Variance"
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Thu, 13 Mar 2008 04:28:45 -0500 (EST)
• References: <fr8b97$h2s$1@smc.vnet.net>

Elements wrote:
> Greeting all
> I'm puzzled by the function "Variance". We can learn how to calculate
> variance from this page:http://mathworld.wolfram.com/SampleVariance.html.
> For example, calculate the sample variance of {1,2,3}. the average of
> {1,2,3} is 2, then the variance should be ((1-2)^2+(2-2)^2+(3-2)^2)/3=2/3.
> But mathematica gives that:
> 
> In[10]:= Variance[{1.0,2.0,3.0}]
> Out[10]= 1.
> 
> Why??
There are two formulae for variance, one where you know the true mean - 
which you have used - where you divide by N, and another where you can 
only estimate the mean from the data available, where it is appropriate 
to divide by (N-1) to obtain an unbiased estimate of the true variance. 
It is this formula that Mathematica has used.

David Bailey
http://www.dbaileyconsultancy.co.uk