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Re: Puzzled by the "Variance"

• To: mathgroup at smc.vnet.net
• Subject: [mg86542] Re: Puzzled by the "Variance"
• From: Bill Rowe <readlists at sbcglobal.net>
• Date: Thu, 13 Mar 2008 04:34:11 -0500 (EST)

On 3/12/08 at 5:29 AM, philyer at gmail.com (Elements) wrote:

>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??

Look at the documentation for Variance paying particular note
details in the More Information section.

Specifically, Mathematica computes an unbiased estimate of the
variance which will use n-1 as the divisor (2 in this particular
case). Using n as the divisor is the maximum likelihood estimate
for the variance. You might also see the difference in divisors
referred to as sample variance (n-1) and population variance (n).