Re: Puzzled by the "Variance"
- To: mathgroup at smc.vnet.net
- Subject: [mg86590] Re: Puzzled by the "Variance"
- From: Norbert Marxer <marxer at mec.li>
- Date: Fri, 14 Mar 2008 04:17:03 -0500 (EST)
- References: <200803121029.FAA17511@smc.vnet.net> <frclto$rqs$1@smc.vnet.net>
On 14 Mrz., 02:55, "Jaccard Florian" <Florian.Jacc... at he-arc.ch> wrote: > You've got a lot of very good answers... > > As a complement: > > In earlier versions, you could also ask for the biased (or population) > variance. It still works with v.6, in spice of the fact that it's > considered as "removed"... > > Just write: > > data = {1, 2, 3}; > << "Statistics`" > VarianceMLE[data] > > It gives: 2/3 > > But it's quite dangerous to use "removed" mathematica packages... > > I just don't understand why Wolfram removed this function... In most > other systems, you can ask for both variances! > > Florian Jaccard > > -----Message d'origine----- > De: Elements [mailto:phil... at gmail.com] > Envoy=E9=A0: mercredi, 12. mars 2008 11:29 > =C0=A0: mathgr... at smc.vnet.net > Objet=A0: =A0Puzzled by the "Variance" > > 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 Hello In Mathematica you can use the built-in function CentralMoment[data, 2]. To summarize this post: You have (as was posted by many) to distinguish between the two situations: 1. You do not know the mean and calculate the mean from your data. Then you divide the sum by "n-1" and use Variance[data] to calculate the variance. 2. You know the mean (for the population). Then you divide the sum by "n" and use CentralMoment[data,2] or Needs["Statistics`"]; VarianceMLE[data] to calculate the variance. data = {1, 2, 3}; Variance[data] Needs["Statistics`"]; VarianceMLE[data] CentralMoment[data, 2] I hope this helps. Best Regards Norbert Marxer
- References:
- Puzzled by the "Variance"
- From: Elements <philyer@gmail.com>
- Puzzled by the "Variance"