Prove that the sum of deviations from mean is zero .

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Please find below the solution to the asked query:

Let x1,x2....,xn be real data.let x¯ be arithmertic mean.Prove:i=1nxi- x¯=0Proof:i=1nxi- x¯=x1- x¯+x2- x¯+x3- x¯+......xn- x¯=x1- xin+x2- xin+x3- xin+......xn- xin=x1+x2+x3....+xn-nxin=xi-xi=0Q.E.D

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