A population consists of the following five values 2 2 4 4 a

A population consists of the following five values: 2, 2, 4, 4, and 8.
a. List all samples of size 2, and compute the mean of each sample.
b. Compute the mean of the distribution of sample means and the population mean. Compare the two values.

Solution

the sample are (2,2);(2,4);(2,4);(2,8),(2,2);(2,4);(2,4);(2,8);(4,2)(4,2);(4,4);(4,8);(4,2)(4,2);(4,4);(4,8),(8,2);(8,2),(8,4),(8,4)

the mean of the above sample is as follows

mean of (2,2)=2

mean of(2,4)=3

mean of(2,4)= 3

mean of ;(2,8)=5

mean of ,(2,2)=2

mean of ;(2,4)=3

mean of (2,4)=3

mean of (2,8)=5

mean of (4,2)=3

mean of (4,2)=3

mean of ;(4,4)=4

mean of (4,8)=6

mean of (4,2)=3

mean of (4,2)=3

mean of (4,4)=4

mean of (4,8)=6

mean of (8,2)=5

mean of (8,2)=5

mean of(8,4),=6

mean of (8,4)=6

mean of sample mean is given by the mean of above means

2,3,3,5,2,3,3,5,3,3,4,6,3,3,4,6,5,5,6,6

is 80/20=4

population mean is given by mean of 2,2,4,4,8

that is 20/5=4

both the mean are same