Re: Puzzled by the "Variance"

• To: mathgroup at smc.vnet.net
• Subject: [mg86544] Re: Puzzled by the "Variance"
• From: "Nasser Abbasi" <nma at 12000.org>
• Date: Thu, 13 Mar 2008 04:34:34 -0500 (EST)
• References: <fr8b97\$h2s\$1@smc.vnet.net>
• Reply-to: "Nasser Abbasi" <nma at 12000.org>

```"Elements" <philyer at gmail.com> wrote in message
news:fr8b97\$h2s\$1 at smc.vnet.net...
> Greeting all
> I'm puzzled by the function "Variance". We can learn how to calculate
> 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 uses the assumption that the data is a sample (size is small),
hence it gives the sample variance, not population variance.

The formula in this case changes. You need to divide by (n-1) not (n) where
n is the sample size.

In[5]:= r = {1., 2., 3.};
Variance[r]
Out[6]= 1.

In[13]:= m = Mean[r];
n = Length[r];
Sum[(r[[i]] - m)^2, {i, 1, n}]/(n - 1)
Out[15]= 1.

Nasser

```

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