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?

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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?

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Answer 1 · 2017-05-10T20:56:35

$σ (C) = σ (A) + σ (B)$ $\sigma(C) =\sigma(A) +\sigma(B)$

Explanation:

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

according to expectation $V A R (A + B) = V A R (A) + V A R (B)$ $VAR(A+B) = VAR(A)+VAR(B)$ therefore $σ (A + B) = \sqrt{V A R (A + B)} = \sqrt{V A R (A)} + \sqrt{V A R (B)}$ $\sigma(A+B) = sqrt(VAR(A+B)) = sqrt(VAR(A)) + sqrt(VAR(B))$

so. ..
$σ (C) = σ (A) + σ (B)$ $\sigma(C) =\sigma(A) +\sigma(B)$

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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?

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