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Standard deviation of series of trials

  1. May 2, 2013 #1
    Say we want to saw ten planks and we have two methods available - one is sawing them all at once, ensuring they're all exactly uniform length. The other method is sawing them individually. Either method has EV of 1m and a standard deviation of 0.005m. I want to find the standard deviation of both methods.

    In other words, given a random variable X, I guess what we're trying to figure out is SD(10X) and SD(X1 + X2 + ... + X10).

    I'm not sure how to calculate the second one. Anyone want to give me a push? :S
     
  2. jcsd
  3. May 2, 2013 #2

    CompuChip

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    [tex]\operatorname{SD}(A + B + \cdots + Z) = \sqrt{\operatorname{SD}(A)^2 + \operatorname{SD}(B)^2 + \cdots + \operatorname{SD}(Z)^2}[/tex]

    What this basically says is that the variance Var(X) = SD(X)² is linear:
    [tex]\operatorname{Var}(A + B + \cdots + Z) = \operatorname{Var}(A) + \operatorname{Var}(B) + \cdots + \operatorname{Var}(Z)[/tex]

    Also note that by setting A = B = ... = X you can actually derive the result for SD(10X).
     
  4. May 2, 2013 #3
    Thanks a ton!
     
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