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在《统计初步》中我们学习了反映一组数据平均水平和刻划一组数据波动大小的两个概念——平均数x珚和方差s2.若一组数据为x1,x2,x3,…,xn,则x珚=1n x1+x2+…+x(n)或x1+x2+…+xn=nx珚;s2=1n[(x1-x珚)2+(x2-x珚)2+…+(xn-x珚)2].上式右端展开,可以得到s2=1n(x21+x22+…+x2n)-x珚2.根据上面的公式,我们不难得到关于平均数和方差的如下性质:性质1设一组数据x1,x2,…,xm的平均数为x珚,另一组数据y1,y2,…,yn的平均数为y珔(x珚≠y珔),则新数据x1,x2,…,xm,y1,y2,
In “Preliminary Statistics,” we have studied two concepts that reflect the average level of a set of data and the size of a set of data - the average x 珚 and the variance s2. If a set of data is x1, x2, x3, ..., then x 珚 = 1n x1 + x2 + ... + x (n) or x1 + x2 + ... + xn = nx 珚; s2 = 1n [(x1-x 珚) 2+ (x2-x 珚) 2 + we can get s2 = 1n (x21 + x22 + ... + x2n) -x 珚 2. According to the above formula, it is not hard to get the following properties about mean and variance: Properties 1 Let the average of one set of data x1, x2, ..., xm be x 珚 and the average of the other set of data y1, y2, ..., yn be y 珔 (x 珚 ≠ y 珔), the new data x1, x2 , ..., xm, y1, y2,