Given-that-x-xi-n-1-and-y-yi-n-2-show-that-x-c-n-1-x-n-2-y-n-1-n-2-

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

G i v e n t h a t \bar{x} = \frac{Σ x i}{n_{1}} a n d \bar{y} = \frac{Σ y i}{n_{2}}

s h o w t h a t

{\bar{x}}_{c} = \frac{n_{1} (\bar{x}) + n_{2} (\bar{y})}{n_{1} + n_{2}}

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

n_{1} \bar{x} = x_{1} + x_{2} + \dots + x_{n_{1}}

n_{2} \bar{y} = y_{1} + y_{2} + \dots + y_{n_{2}}

\frac{x_{1} + x_{2} + \dots + x_{n_{1}} + y_{1} + y_{2} + \dots y_{n_{2}}}{n_{1} + n_{2}}

= \frac{n_{1} \bar{x} + n_{2} \bar{y}}{n_{1} + n_{2}}