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Radius of Deviation?

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TheMoonlitKnight

TheMoonlitKnight

Structural
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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)?

Wikipedia said:
"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.
Click to expand...

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...
 
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"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.

TTFN
faq731-376
7ofakss

Need help writing a question or understanding a reply? forum1529
 
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Just found this:

Engineering Mechanics: Statics By I. C. Jong said:
A centroidal radius of gyration represents the standard deviation of the distances of the area elements from the centroidal axis
Click to expand...

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


New here? Try reading these, they might help FAQ731-376
 
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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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