Chris Chiu wrote:
>
> Dear friends:
>
> Does anyone know / remember how to obtain the standard deviation of a set
> of numbers given only a frequency table?
>
> e.g.,
> x f(x)
> 0 0.2
> 1 0.3
> 2 0.2
> 3 0.2
> 4 0.1
(0) This is not a frequency table, it's a relative frequency table.
Such a representation is appropriate for _populations_ so we shouldn't
worry about the "N-1"
correction, which is just as well since we cannot find N from these
data.
(1) Compute the mean as sum [x * f(x)] : 0x0.2 + ...
(2) Compute the deviations from the mean:
> x-mu f(x)
> -1.7 0.2
...
(3) Compute the mean square:
(-1.7)^2 * 0.2 + ...
(3a) If this is a poorly-condensed representation of a small sample,
YOU WILL NEED TO GET N FROM SOMEWHERE. Then multiply by N and divide by
N-1. And pencil in some time on your planner to tell off the person who
mangled the data. Or combine the two exercises by making _them_ do the
correction...
(4) Take the square root, get sigma.
-Robert Dawson
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