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Question: Which of the following is a property of sampling distribution?
I. Mean of sampling distribution equals population mean.
II. Sample mean comes closer to population mean than any other unbiased mean.
III. As sample size increases, variation of sample mean from population mean increases.


A ) I and II only
B ) III only
C ) all are correct
D ) II and III only

Steps to derive

1 Statement I: If the sample taken is the exact representation of the population then the mean of sampling distribution equals population mean.

2 Statement II: Sample mean comes closer to population mean than any other unbiased mean. It is the minimum variance or efficiency of sampling distribution.

3 Statement III: As sample size increases, variation of sample mean from population mean decreases (does not increase).

4 So, only statements I and II are the properties of sampling distribution.



Hence the right answer is Option A

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