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Question Number 38059 by suryavi last updated on 21/Jun/18

$$Provethat\mathrm{\Sigma }(x_i-\stackrel{-}{x})=0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jun/18

$$\mathrm{\Sigma }(x_i-\stackrel{-}{x})$$$$\stackrel{-}{x}=\frac{\mathrm{\Sigma }{x}_i}{n}$$$$\mathrm{\Sigma }(x_i-\stackrel{-}{x})$$$$=(x_1-\stackrel{-}{x})+(x_2-\stackrel{-}{x})+(x_3-\stackrel{-}{x})+...+(x_n-\stackrel{-}{x})$$$$=(x_1+x_2+x_3+....)-(\stackrel{-}{x}+\stackrel{-}{x}+...+\stackrel{-}{x})$$$$=\frac{\mathrm{\Sigma }{x}_i}{n}\times n-n\stackrel{-}{x}$$$$=n\stackrel{-}{x}-n\stackrel{-}{x}$$$$=0$$

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