Re: Correlation Between Mean and Standard Deviation

On Jun 13, 5:03 pm, Graham Ashe <knight_arm...@xxxxxxxxx> wrote:
[...]
Both sets of my data have a theoretical minimum and maximum value
of 0 and 1 respectively (it can't be more or less than that).
What are being measured are the aesthetic values of different
manifestations of two similar types of objects.
[...]

If all the data values must be between 0 and 1, then the mean must
also be between 0 and 1 (which is obvous), and the maximum possible
standard deviation = sqrt[mean*(1-mean)], which is not so obvious.
If you plot the maximum possible s.d. as a function of the mean,
you'll see it's a semicircle with a radius of .5, centered at mean
= .5, s.d. = 0. When the mean is extreme, the s.d. must be small.

So yes, the numbers in the data set with the larger s.d. are more
variable, but whether or not that increased variability is "real"
or is merely an artifact of the measurement scale depends on the
details of the situation.
.