Re: [Phys-L] Statistics question

[John Denker <jsd@av8n.com>]

On 08/24/2012 03:11 PM, Paul Nord wrote:

> don't we generally use the standard deviation and not the HWHM?
> Standard deviation is slightly smaller.

What do you mean by "we", Kemosabe?
 -- Sometimes there are excellent reasons for using the HWHM.
 -- Sometimes there are excellent reasons for using the standard deviation.
 -- Sometimes there are excellent reasons for using both ... or neither.

The only rule here is:  Say what you mean, and mean what you say.

> Is the standard deviation still defined for any set of measurements
> even it they are widely scattered?

Yes.  There is an utterly straightforward mathematical definition
of standard deviation.

> Can I call .... the standard deviation even though a normal
> distribution clearly will not fit the data?

Yes.  Non-normal distributions have perfectly well defined
standard deviations.

Whether the standard deviation of some wacky distribution tells 
you anything /interesting/ is another question.  Sometimes it
does ... sometimes it doesn't.