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Re: [Phys-L] Statistics question

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

Tossing more gas on the fire...

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

For example, if I measure the wavelength of the sodium yellow doublet, I can calculate a mean frequency for the spectrum. And I can calculate the root mean squared difference of the frequencies of all other measured photons observed. Can I call that the standard deviation even though a normal distribution clearly will not fit the data?


On Aug 24, 2012, at 3:23 PM, John Denker wrote:

On 08/24/2012 11:35 AM, Paul Nord wrote:
Do you say "half-width" or Full Width at Half Max (FWHM)? And what
does it mean?

Well, the rule is simple: Say what you mean, and mean what you say.

If you mean FWHM, say FWHM. If you mean HWHM, say HWHM.

For typical well-behaved theoretical distributions, such as triangular,
rectangular, gaussian, et cetera, the maximum is well defined, and
hence both the FWHM and HWHM are well defined.

a) Note that the standard deviation is typically slightly smaller than
the HWHM ... and therefore much closer to the HWHM than to the FWHM.

b) Also, if you are using the "±" notation, it makes sense to talk
about ± HWHM (not ± FWHM).

For these two reasons, I find myself talking about the HWHM more often
than the FWHM ...... but if you have a reason to talk about the FWHM
that's perfectly OK. Say what you mean, and mean what you say.

For pictures and formulas pertaining to some familiar distributions,


For an empirical distribution, such as the histogram of arbitrary data,
you might find that the maximum, FWHM, and HWHM are not very well
behaved. The mean and standard deviation are more likely to be well
behaved, but even that is not a sure thing.


If this isn't the answer that was wanted, please as a more specific
Forum for Physics Educators