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Radius of Deviation?

Radius of Deviation?

Radius of Deviation?

(OP)
I recently noticed how similar the equations for the radius of gyration and the standard deviation (for a population) appear.

Can anybody explain their similarities (and maybe differences)?

Quote (Wikipedia)

"It (the Radius of Gyration) also can be referred to as the radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that axis.

Does it follow that the standard deviation can be referred to as the distance from a given mean at which the population could be concentrated without altering the precision around that mean?

A clear lack of similarity I see is, in mechanics, a higher radius of gyration is desirable, whereas in statistics a lower standard deviation is desirable.

Oh the things we do on a weekend when our significant other is out of town...

RE: Radius of Deviation?

"Does it follow that the standard deviation can be referred to as the distance from a given mean at which the population could be concentrated without altering the precision around that mean?"

No. The standard deviation results in the capturing 68.27% of a Gaussian probability distribution. I have no idea why they would be confluent at all.

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RE: Radius of Deviation?

(OP)
Just found this:

Quote (Engineering Mechanics: Statics By I. C. Jong, B. G. Rogers)

A centroidal radius of gyration represents the standard deviation of the distances of the area elements from the centroidal axis

This text says that they are. If N (the population or sample) is analogous to 'area' then it makes sense.

RE: Radius of Deviation?

"in mechanics, a higher radius of gyration is desirable"

Sometimes, not always. For example many column inches have been wasted on the preference for low polar moment of inertias for racing cars.

Cheers

Greg Locock


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RE: Radius of Deviation?

(OP)
Good catch. I am from a building structures perspective, and you don't see that too often. I should have been more specific. :)

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