Re: Variance as central moment

On 28 Mar 2006 03:38:02 -0800, shehry@xxxxxxxxx wrote:

Hi,

i am new to statistics and i was reading the 'variance' and the
'central moment' pages at wikipedia. I read that variance was the
second central moment. And that the idea of the central moments came in
from the moment theory in physics.

First and second *moments*, and so on, are named from
the power of x, x^1, x^2, x^3, ... , which uses the raw values.
You can look at the total or (more often) the average.

The "central" moment is a re-definition that centers around
the mean. It is also useful, for statisticians at least, to
use versions of the 3rd-and-higher central moments that are
"standardized" to be dimensionless.



i have been trying to relate the two concepts (moment in physics and
moment in stats) but i am still not sure. the way i see it, variance
gives the spread about the mean position (the axis of rotation). but is
that the only relationship between the physics and stats concept???

plus i read that the third and the fourth central moments are skewness
and kurtosis. can i get any help concerning regarding those two as
well. i would really like to know how they came to be known as the
third and fourth central moments.

There are several formulas for skewness and kurtosis,
which vary in how they are standardized. As I mentioned,
"3rd" and "4th" are the powers.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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