analogy: probability :: mechanics

[gusl]

mean :: center of mass
variance (i.e. second moment about the mean) :: moment of inertia about the center of mass

This was suggested by Stats professor on Monday's class. I filled in the second analogy.

Comments

[jcreed.livejournal.com]

I thought these were pretty standard?

[gustavolacerda.livejournal.com]

how did you learn about them?
They sure deserve to be... but how many people know basic mechanics as well as basic statistics? You'd hope all engineers and physicists would.

[jcreed.livejournal.com]

dunno, I don't remember a time I didn't think of them as the same concept. The center of mass just *is* the mean of the mass distribution. Likewise I have always thought of "moment" as a funny concept-unto-itself that I can only approach through its applications in statistics and physics.

[bhudson.livejournal.com]

The first is standard to me, to the point that I use them synonymously; but both my stats and mechanics backgrounds are weak so the second is just something I rediscover once in a while.

I should mention that the first relation was taught to me in high school.

[stepleton.livejournal.com]

I knew the first property but wasn't really aware of the second. Most of this may have to do with how long it's been since I've been exposed to mechanics.

Perhaps this is why I can't help but think, for the second property: so what? The first one gives me a nice mental picture of what taking a mean is like: I can imagine having a dataset and hanging little weights from all the points, then finding the balance point. This makes it easy for me to understand that if I have an outlier, its arm is very far from the center, and accordingly it will have a big impact on the mean. That's an important thing to know.

Ah, and so yes, that's the utility of thinking about variance this way. If a dataset has a large variance, then its moment of inertia is also larger, and so an outlier weight would have to have an even greater arm to have an effect. Well, that's easy to visualize. Jolly good.

Back to work...