s^2=1/n[(x1-x)^2+(x2-x)^2+…+(xn-x)^2] =1/n(x1^2+x2^2+…+xn^2+nx^2-2x1x-2x2x-…-2xnx)∵x=(x1+x2+…+xn)/n∴nx=x1+x2+…+xn∴nx^2=(x1+x2+…+xn)x∴s^2=1/n(x1^2+x2^2+…+xn^2+nx^2-2nx^2) =1/n(x1^2+x2^...