平均数、方差是统计初步中的重要概念,它有两个易懂、实用的性质: 若n个数据x1,x2,……,xn的平均数是x,方差为S2,那么: 1.n个数据x1+a,x2+a,……,xn+a的平均数是x+a,方差不变; 2.n个数据kx1,kx2,……,kxn(k≠0)的平均数是kx,方差是k2S2. 证明这两个性质并不难: 证明:∵x1,x2,……,xn的平均数、方差 The average and variance are important concepts in the preliminary statistics. It has two easy-to-understand and practical properties: If the average number of n data x1, x2, ..., xn is x and the variance is S2, then: 1.n The average number of data x1+a, x2+a, ..., xn+a is x+a, and the variance is constant; 2. The average number of n data kx1, kx2, ..., kxn(k≠0) is Kx, the variance is k2S2. Proving these two properties is not difficult: Proof: mean, variance of ∵x1,x2,...,xn