Question

一道初中方差题如果样本X1-2,X2-2,...,Xn-2的平均数为10,方差为24,则样本X1+3,X2+3,...,

Answer 1

根据平均数和方差的定义可知

[(x1-2)+(x2-2)+...+(xn-2)]/n=10

则有

[(x1+3)+(x2+3)+...+(xn+3)]/n

=[(x1-2+5)+(x2-2+5)+...+(xn-2+5)]/n

=[(x1-2)+(x2-2)+...+(xn-2)+5n]/n

=10+5

=15

[(x1+3-15)²+(x2+3-15)²+...+(xn+3-2)²]/n

=[(x1-2-10)²+(x2-2-10)²+...+(xn-2-10)²]/n

=24

xn+3的平均数是15,方差不变,依然是24～

原题的方差应该是2.4,不是24

都一样的,方差不变,平均数是15,选B