Xiao Ming finds it troublesome to use the formula in the book to calculate the variance of a group of data. Xiao Ming, who is good at using his brain, finds it Xiao Ming finds it troublesome to use the formula in the book to calculate the variance of a group of data. He is good at using his brain to find the simplified formula s ^ 2 = 1 / n [(x1 ^ 2 + x2 ^ 2 +...) +When n = 3, the formula of transformation is s ^ 2 = 1 / n [(x'1 ^ 2 + X'1 ^ 2 +...] +Nx'n ^ 2) - NX '^ 2], where x'1 = x1-a, X'2 = x2-a, X'n = xn-a, is his idea correct? If correct, please prove. | Math enthusiast | Mathematical art

Xiao Ming finds it troublesome to use the formula in the book to calculate the variance of a group of data. Xiao Ming, who is good at using his brain, finds it Xiao Ming finds it troublesome to use the formula in the book to calculate the variance of a group of data. He is good at using his brain to find the simplified formula s ^ 2 = 1 / n [(x1 ^ 2 + x2 ^ 2 +...) +When n = 3, the formula of transformation is s ^ 2 = 1 / n [(x'1 ^ 2 + X'1 ^ 2 +...] +Nx'n ^ 2) - NX '^ 2], where x'1 = x1-a, X'2 = x2-a, X'n = xn-a, is his idea correct? If correct, please prove.

S^2=1/n*[(x1-x')^2+(x2-x')^2+(x3-x')^2]=1/n*[[(x1-a)-(x'-a)]^2+[(x3-a)-(x'-a)]^2+[(x3-a)-(x'-a)]^2]=1/n*[[(x1-a)^2-2(x1-a)(x'-a)+(x'-a)^2]+[(x2-a)^2-2(x2-a)(x'-a)+(x'-a)^2+[(x3-a)^2-2(x3-a)(x'-a)+(x'-...

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