Question

If C is the union of A and B, how do you calculate the standard deviation of population C if you know the standard deviations of A and B? What if A and B are of different sizes?

Answer 1

`\sigma(C) =\sigma(A) +\sigma(B)`

Explanation:

if C = A U B then you can conclude that it should be equivalent to ask what is `\sigma(A+B)`

according to expectation `VAR(A+B) = VAR(A)+VAR(B)` therefore `\sigma(A+B) = sqrt(VAR(A+B)) = sqrt(VAR(A)) + sqrt(VAR(B))`

so. ..
`\sigma(C) =\sigma(A) +\sigma(B)`