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
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

--
This e-mail may contain trade secrets or privileged, undisclosed or
otherwise confidential information. If you are not the intended
recipient and  have received this e-mail in error, you are hereby
notified that any review, copying or distribution of it is strictly
prohibited. Please inform us immediately and destroy the original