某次数学检测满分为100分,某班的平均成绩为75分,方差为40,若把每位同学的成绩按满分为120分进行换算,则换算后的平
1个回答

设成绩分别为:x 1,x 2,…x n

.

x =

1

n (x 1+x 2+x 3…+x n)=75,

方差S 2=

1

n [(x 1-

.

x ) 2+(x 2-

.

x ) 2+…+(x n-

.

x ) 2]=40,

换算后成绩分别为1.2x 1,1.2x 2,…1.2x n

.

x =

1

n (1.2x 1+1.2x 2+1.2x 3…+1.2x n)=1.2×

1

n (x 1+x 2+x 3…+x n)=1.2×75=90,

方差S 2 2=

1

n [(1.2x 1-1.2

.

x ) 2+(1.2x 2-1.2

.

x ) 2+…+(1.2x n-1.2

.

x ) 2]=1.2 2×

1

n [(x 1-

.

x ) 2+(x 2-

.

x ) 2+…+(x n-

.

x ) 2]=1.44×40=57.6,

故答案为:90,57.6.