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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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