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

thanks in advance!