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?

May 10, 2017

$\setminus \sigma \left(C\right) = \setminus \sigma \left(A\right) + \setminus \sigma \left(B\right)$

Explanation:

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

according to expectation $V A R \left(A + B\right) = V A R \left(A\right) + V A R \left(B\right)$ therefore $\setminus \sigma \left(A + B\right) = \sqrt{V A R \left(A + B\right)} = \sqrt{V A R \left(A\right)} + \sqrt{V A R \left(B\right)}$

so. ..
$\setminus \sigma \left(C\right) = \setminus \sigma \left(A\right) + \setminus \sigma \left(B\right)$