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Question Number 42058 by Rio Michael last updated on 17/Aug/18

$$Giventhat\overline{\mathrm{x}}=\frac{\mathrm{\Sigma }\mathrm{x}i}{n_1}and\overline{y}=\frac{\mathrm{\Sigma }yi}{n_2}$$$$showthat$$$${\overline{\mathrm{x}}}_c=\frac{n_1\left(\overline{\mathrm{x}}\right)+n_2\left(\overline{y}\right)}{n_1+n_2}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18

$$n_1\stackrel{-}{x}=x_1+x_2+...+x_{n_1}$$$$n_2\stackrel{-}{y}=y_1+y_2+...+y_{n_2}$$$$\frac{x_1+x_2+...+x_{n_1}+y_1+y_2+...y_{n_2}}{n_1+n_2}$$$$=\frac{n_1\stackrel{-}{x}+n_2\stackrel{-}{y}}{n_1+n_2}$$

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