Answer to Question #318550 in Statistics and Probability for ana

Question

A population consists of the four numbers 3,7,11,15.Consider all possible samples of size two which can be drawn with replacement from this population

Answer 1

Number N= N!/n!(N-n)!

=4!/2!(4-2)!

=(3*4)/2 =6

N=6

samples are

3,7

3,11

3,15

7,11

7,15

11,15

mean =(3+7+11+15)/4 =36/4=9

the mean is 9

standard deviation= ​sqrt{1/3((3-9)² +(7-9)² +(11-9)² +(15-9)²}

=​ sqrt{1/3(36+4+4+36)}

=​ sqrt{1/3(80)}

=5.164

standard deviation is 5.164