relation between standard deviation and the mean?

Question

what is the relation between standard deviation and the mean in statistics

Answer 1

They are really not dependent on each other, rather they are characteristics of the distribution used.

There is a metric called the coefficient of variance which connects the two in a useful way.

The coefficient of variance is the ratio of the standard deviation to the mean.

Here is a Wikipidia entry covering this metric in depth:

http://en.wikipedia.org/wiki/Coefficient_of_variation

Answer 2

For a random variable X, the mean is E(X) (expected value).
Variance = E[(X-m)^2] = E(X^2) - m^2 where m is the mean
and standard deviation is square roots of variance.
They are not really related, but the standard deviation is a measure of how much the data differs from the mean.