Re: variance (mg86506)
- To: mathgroup at smc.vnet.net
- Subject: [mg86609] Re: variance (mg86506)
- From: Sebastian Meznaric <meznaric at gmail.com>
- Date: Sat, 15 Mar 2008 03:08:30 -0500 (EST)
- References: <frasfq$1m4$1@smc.vnet.net>
On Mar 13, 9:34 am, Kowalczyk-Schr=F6der <HB-Kowalczyk-Schroed...@t- online.de> 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>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 > > Mathematica divides by (N-1) - like as far as I know all programs- This > is correct if you have only a sample and not the whole. You can look up > the reason for this and the derivation in some book about statistics. > > Sincerely, > J. Schroeder > ############################ > Dr. Joerg Schroeder > Bremen Hi. Mathematica calculates the unbiased estimator for the variance based on your sample. This means it actually calculates ((1-2)^2+(2-2)^2+(3-2)^2)/2. In general, the unbiased estimator is 1/ (N-1) sum((x_i - mean)^2). All you need to do is multiply with (N-1)/N to obtain your version of the variance. So in your case N=3 so 1*2/3=2/3.