On 21 Aug 2001, RFerreira wrote [edited]:
> The formula [for] the Standard Deviation, SD=((x-mean)^2/(n-1))^0.5,
> can be applied to any data set. [With] that value we know two things
> about the set: mean and SD. With these two values we can have one
> powerful intuitive use to them: The "centre" of the set is the mean
> and 68% of values are in the interval [mean-SD to mean+SD], IF the set
> have Normal Distribution. If the set distribution is NOT Normal, what
> intuitive use have the values?
That of course depends on what the distribution actually is. Some
textbooks these days write of "empirical distributions", by which is
meant any approximately symmetrical "mound-shaped" distribution, and for
which approximately 2/3 of the distribution falls within 1 SD of the
mean, approximately 95% within 2 SD, and nearly all of it (99.7% if it's
normal) with 3 SD. These descriptions apply (with suitable hand-waving
around the "approximately" parts) to lots of real data, and to a number
of theoretical distributions as well -- the ones that are commonly
treated by "normal approximations".
> Other intuitive definition as that I see in RadioFrequency: The
> bandwidth of one amplifier is between the frequencies where the power
> decrease to half of the power at the central frequency.
Which doubtless explains why a nearby radio station interferes
distressingly with my favorite classical music station broadcasting from
Boston.
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