Re: Variance as central moment

shehry@xxxxxxxxx wrote in news:1143545882.002398.285910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

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.

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???


The first point in physics where you encounter "moments" is in considering
levers. Later you encounter the term when considering the dynamics of solid
bodies.

The center of mass (first mass moment) is analogous to the statistical
concept of arithmetic mean. COM is found by minimizing sum of mass at point
times distance from center.

Moments of inertia are second mass moments and are calculated by summing or
integrating the product of mass at a point by squared distance from an axis
of rotation. This has a mathematical similarity to the variance.

http://www.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_2.html
http://kwon3d.com/theory/moi/moi.html

Physics has been a major motivator of statistical advances over the centuries.
One might have an interesting debate which of insurance, gambling, or physics
could claim to have motivated the greatest advances in statistics. When I open
up the Table of Contents from Pearson's "History of Statistics in the 17th and
18th Centuries" I see many names of mathematicians (Laplace, Poisson, Lagrange,
D'Alembert, Euler) who I first knew for their contributions to physical
theory.

--
David Winsemius
.

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