How do you compute one sigma deviation?

Let x denote the values of the variable in question.

Suppose there are n observations.

Let Sx = the sum of all the values.

then the mean of x, Mx = Sx/n

Let Sxx = the sum of all the squares of the values.

The Vx (= the variance of x) is Sxx - (Mx)^2

and sigma(x) = sqrt(Vx).

Therefore one sigma deviation, relative to the mean,

= Mx - sigma(x), Mx + sigma(x).