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Adding Variance

  1. Sep 6, 2011 #1
    Hi

    If I have measured the resonance frequency of three sets of resonators and calculated the mean, variance and standard deviation for each set. How do I add the three variances and standard deviations to get an overall variance and standard deviation?

    Well, I know that the standard deviation is the square root of the variance and therefore I only need to know how to calculate the overall variance.

    I hope that someone can help me with my problem. Thanks in advance.

    Best regards
    Tom
     
  2. jcsd
  3. Sep 6, 2011 #2
    If your three resonance frequencies are independent, then

    [tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)[/tex]

    If not, then

    [tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)+2Cov(X_1,X_2)+2Cos(X_2,X_3)+2Cov(X_1,X_2)[/tex]
     
  4. Sep 6, 2011 #3

    chiro

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    Science Advisor

    Is your last term meant to be Cov(X_1,X_3)?
     
  5. Sep 7, 2011 #4
    Thanks

    One clarifying question. If I have an infinite number of sets and I then add the variances for all the sets then the variance and hence the standard deviation will also be infinite?
     
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