数据X1 X2 X3 X4 的平均数是2,则3X1-1 3X2-1 3X3-1 3X4-1的平均数是5 方差是18 怎么算出来的?

问题描述:

数据X1 X2 X3 X4 的平均数是2,则3X1-1 3X2-1 3X3-1 3X4-1的平均数是5 方差是18 怎么算出来的?

E1=(X1+ X2 +X3 +X4 )/4=2 S1=(2-X1)^2+(2-X2)^2+(2-X3)^2+(2-X4)^2=2 E2=(3X1-1+3X2-1+3X3-1+3X4-1)/4=3(X1+ X2 +X3 +X4 )/4-1=3*2-1=5 S2=[5-(3X1-1)]^2+[5-(3X2-1)]^2+[5-(3X3-1)]^2+[5-(3X4-1)]^2 =(6-3X1)^2+(6-3X2)^2+(6-3X3)^2+(6-3X4)^2 =9(1-X1)^2+9(1-X2)^2+9(1-X3)^2+9(1-X4)^2 =9[(1-X1)^2+(1-X2)^2+(1-X3)^2+(1-X4)^2] =9*2=18