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 -- 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 transmittal from your system. Thank you for your co-operation.