Question 283898
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.
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Using the 1st "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
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Using the 2nd "2":
2,2: mean = 2
2,4: mean = 3
2,4: mean = 3
2,8: mean = 5
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Using the 1st "4":
4,2: = 3
4,2: = 38,2
4,4: = 4
4,8: = 6
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Using the 2nd "4:
4,2: = 3
4,2: = 3
4,4: = 4
4,8: = 6
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Using the "8":
8,2: = 5
8,2: = 5
8,4: = 6
8,4: = 6
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b. Compute the mean of the disbribution of sample means 
Find the mean of {2,3,3,5,2,3,3,5,3,3,4,6,3,3,4,6,5,5,6,6} 
= (13+13+16+16+22)/20 = (26+32+22)/20 = 80/20 = 4
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compute the population mean
Find the mean of {2,2,4,4,and 8} = 20/5 = 4
. compare the two values.
The mean of the sample means is the same as the mean of the population.
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c. Compare the dispersion in the population with that of the sample mean.
Range of the population is 8-2 = 6
Range of the sample means is 6-2 = 4
The sample means are less dispersed than the population.
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Cheers,
Stan H.