数理统计证明,

左=[1/2n(n-1)]∑∑(xi-xj)^2=[1/2n(n-1)]∑∑[xi^2+xj^2-2xixj]=[1/2n(n-1)](n∑xi^2+n∑xj^2-2∑∑xixj)
=[1/2n(n-1)](2n∑xi^2-2(∑xi)^2)=∑xi^2/(n-1) -n/(n-1)(x(bar))^2=S^2