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Re: Puzzled by the "Variance"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86528] Re: [mg86506] Puzzled by the "Variance"
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 13 Mar 2008 04:31:33 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200803121029.FAA17511@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

"Variance", as being used in Mathematica and in MathWorld, is actually 
"sample variance", as distinct from "population variance".  What you 
calculated to be 2/3 is actually the population variance.

The difference:

   sampleVar[x_] := Total[(#^2 &) /@ (x - Mean@x)]/(Length[x] - 1)
   populationVar[x_] := Total[(#^2 &) /@ (x - Mean@x)]/Length[x]

   { sampleVar[{1,2,3}], populationVar[{1,2,3}] } // InputForm
{1, 2/3}

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??

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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