Given the standard deviation, mean & N of two groups, how can i combine the two std deviations?

Answer 1

(sd)^2 = Σ(x - μ)^2 / (n-1)
So from the s.d. and number of each group you can retrieve Σ(x - μ)^2
= Σx^2 - 2μ Σx + nμ^2
= Σx^2 - nμ^2 (since Σx = nμ).
Once you have Σx^2 for each group, add them together to get Σx^2 for the combined group.

Let the mean and number for the first group be μ1 and n1, and for the second group μ2 and n2. Let μ and n be mean and number for the combined group (n = n1 + n2). The mean of the combined group is μ = (n1μ1 + n2μ2) / n.

Then the s.d. of the combined group is just
s.d = √ ((Σx^2 - nμ^2) / (n-1)).