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Math Help - easy standard deviation problem

  1. #1
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    easy standard deviation problem

    If the frequency ,mean and standard deviation of two sets of observations be denoted by n_{1},\bar{x_{1}}, \sigma_{1} and n_{2},\bar{x_{2}}, \sigma_{2} respectively, then prove that N{\sigma}^2=n_{1}{\sigma_{1}}^2+n_{2}{\sigma_{2}}^  2+n_{1}{d_{1}}^2+n_{2}{d_{2}}^2 where, N=n_{1}+n_{2},d_{1}=\bar{x_{1}}-M, d_{2}=\bar{x_{2}}-M and M,\sigma are the mean and standard deviation of the combined set of observations.


    thanks in advance!
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  2. #2
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    Re: easy standard deviation problem

    Hey earthboy.

    Do you know results regarding variances for random variables?

    (Hint: things like Var[aX + bY] = a^2*Var[X] + b^2*Var[Y] if X and Y are independent)
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