easy standard deviation problem

**earthboy** · December 4th 2012, 10:32 PM

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!

**chiro** · December 5th 2012, 04:34 PM

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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