Question

A group of students got the following scores in a test 2,4,6,8, and 10. Consider samples of size 3 that can be drawn from this population. Find the following population mean,variance, and standard deviation

Answer 1

m{2,4,6}=(2+4+6)/3=4

m{2,4,8}=(2+4+8)/3=4.7

m{2,4,10}=(2+4+10)/3=5.3

m{2,6,8}=(2+6+8)/3=5.3

m{2,6,10}=(2+6+10)/3=6

m{2,8,10}=(2+8+10)/3=6.7

m{4,6,8}=(4+6+8)=6

m{4,6,10}=(4+6+10)/3=6.7

m{6,8,10}=(6+8+10)/3=8

f(4)=f(4.7)=f(8)=1/9

f(5.3)=f(6)=f(6.7)=2/9

$E(x)=\sum xf(x)=1/9(4+4.7+8)+2/9(5.3+6+6.7)=1.86+4=5.86$

$\sigma^2=\sum x^2f -( \sum xf)^2=1/9(16+22.09+64)+2/9(28.09+36+44.89)-34.34=11.34+24.22-34.34=1.22$

$\sigma=\sqrt{\sigma^2}=1.1$