Question

x,y,10,11,9的平均数为10,方差为2,问x-y的绝对值该怎么算

Answer 1

(x+y+10+11+9)/5=10

x+y+30=50

x+y=20 (1)

(x-10)^2+(y-10)^2+(10-10)^2+(11-10)^2+(9-10)^2=2*5

(x-10)^2+(y-10)^2+0+1+1=10

(x-10)^2+(y-10)^2=8

x^2-20x+100+y^2-20y+100=8

x^2-20x+y^2-20y=-192 (2)

(2)+20*(1):

x^2+y^2=208 (3)

(1)^2:x^2+2xy+y^2=400 (4)

(4)-(3):2xy=192 (5)

|x-y|^2=x^2+y^2-2xy=(3)-(5)=208-192=16

所以,|x-y|=4