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Math Help - Variance confusion

  1. #1
    psgame_freak
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    Variance confusion

    Im confused with the formulas VAR[f(x)] = a^2VAR(X + b) and Sum of Independent Random VAR(C) = VAR(A) + VAR(B)

    -Adult males of a certain species of animal are known to have a mean weight of 1.3 kg with standard error of .2 kg.

    Q: What is the standard error of the total weight of randomly selected groups of 4 males?

    Now I have 2 solutions with different answers.

    Using VAR[f(x)] = a^2VAR(X + b)

    = 4^2 (.2^2)
    = 0.64 kg
    hence Standard error is 0.8 kg

    Using VAR(C) = VAR(A) + VAR(B)

    = .2^2 + .2^2 + .2^2 + .2^2
    = 0.16 kg
    hence Standard error is 0.4 kg

    Which one is right?
    If its not much to ask, could you give me a link to help me with this?
    How do we choose the constant?
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  2. #2
    Senior Member
    Joined
    Apr 2006
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    Quote Originally Posted by psgame_freak View Post
    Im confused with the formulas VAR[f(x)] = a^2VAR(X + b) and Sum of Independent Random VAR(C) = VAR(A) + VAR(B)

    -Adult males of a certain species of animal are known to have a mean weight of 1.3 kg with standard error of .2 kg.

    Q: What is the standard error of the total weight of randomly selected groups of 4 males?

    Now I have 2 solutions with different answers.

    Using VAR[f(x)] = a^2VAR(X + b)

    = 4^2 (.2^2)
    = 0.64 kg
    hence Standard error is 0.8 kg

    Using VAR(C) = VAR(A) + VAR(B)

    = .2^2 + .2^2 + .2^2 + .2^2
    = 0.16 kg
    hence Standard error is 0.4 kg

    Which one is right?
    If its not much to ask, could you give me a link to help me with this?
    How do we choose the constant?
    Var(4X) = 4^2Var(X) applies to one variable.

    Var(X_1 + X_2 + X_3 + X_4) = Var(X_1) + Var(X_2) + Var(X_3) + Var(X_4) applies to 4 independent variables, which is the case here.

    The second answer is correct.

    Searching on "variance sum independent variables" turns up links with explanations, but I didn't see one that really stood out. How about Variance - Wikipedia, the free encyclopedia?
    Last edited by JakeD; July 30th 2007 at 04:55 AM.
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