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?

Khalfanebw

Khalfanebw

Answered question

2022-09-26

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 & Explanation

arribanti9

arribanti9

Beginner2022-09-27Added 5 answers

Explanation:
if C = A B then you can conclude that it should be equivalent to ask what is σ ( A + B )
according to expectation VAR(A+B)=VAR(A)+VAR(B) therefore σ ( A + B ) = V A R ( A + B ) = V A R ( A ) + V A R ( B )
so.
σ ( C ) = σ ( A ) + σ ( B )

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