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Re: Puzzled by the "Variance"

• To: mathgroup at smc.vnet.net
• Subject: [mg86566] Re: [mg86506] Puzzled by the "Variance"
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Thu, 13 Mar 2008 20:53:10 -0500 (EST)

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??
-- 
Best Wishes!
Yours Sincerely


In the same homepage you cited in the bottom you find the following: 
"The unbiased sample variance s_(N-1)^2 is implemented as 
Variance[list]". That is the reason.

According to this definition your example should be calculated as 
((1-2)^2+(2-2)^2+(3-2)^2)/(3-1)=1, rather than 
((1-2)^2+(2-2)^2+(3-2)^2)/3=2/3

In general, I find the whole explanation of Variance[](as well as its 
notation) to be rather obscure.

Regards.

-- 
Alexei Boulbitch, Dr., habil.
Senior Scientist
IEE S.A.
Material Development,
ZAE Weiergewan
11, rue Edmond Reuter,
L-5326 Contern,
Luxembourg
Tel.: +352 2454-2566
Fax:  +352 2454-3566
e-mail: alexei.boulbitch at iee.lu

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