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Question: A population consists of the five numbers 2, 4, 6, 8 and 10. Consider all the samples of size 2 that can be drawn with replacement from the population. Find the mean of the sampling distribution means. Also find the difference between the population mean and mean of the sampling distribution means.


A ) 5, 0.05
B ) 5, 1
C ) 6, 1.25
D ) 6, zero

Steps to derive

1 Population mean (μ) = 2+4+6+8+105 = 6

2 There are 5 × 5 = 25 samples of size 2 that can be drawn with replacement.

3 The samples are


4 The corresponding means are


5 The mean of the sampling distribution of means is μx = sum of the sample means number of sample means.

6 μx = 15025 = 6

7 The population mean (μ) = mean of the sampling distribution means (μx)

8 So, the difference between population mean and the sampling distribution means is zero.



Hence the right answer is Option D

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