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Re: Puzzled by the "Variance"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86549] Re: Puzzled by the "Variance"
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 13 Mar 2008 04:35:30 -0500 (EST)
  • References: <fr8b97$h2s$1@smc.vnet.net>


Hi,

please read the whole article and distinguish between sample variance 

and population variance (also the name are often used confusingly).

Usually one wants to guess what the variance of the population sigma^2 

(the true variance) is. The formula

1/n Sum[(xi-Mean[x])^2]

gives a biased etimate. That is if n->Infinity we do not get the true 

variance. However,

1/(n-1) Sum[(xi-Mean[x])^2]

is not biased and is to be prefered.

Therefore, mathematica does the right thing.

hope this helps, Daniel



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??




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