Question

What is a sampling distribution of means? How is it created and what is it used for?

Answer 1

Sampling distribution is a probability distribution of sample mean. For example, suppose {1,2,3,4} is a set of population units. So the size of populatio, N=4. Now we draw sample of size 2 without replacement technique from this population and the following table shows the sampling distribution of sample mean:

Serial no.	Possible samples	Sample mean=
1.	(1,2)	1.5	1/6
2.	(1,3)	2	1/6
3.	(1,4)	2.5	1/6
4.	(2,3)	2.5	1/6
5.	(2,4)	3	1/6
6.	(3,4)	3.5	1/6

Hence the sampling distribution of is

	1.5	2	2.5	3	3.5
	1/6	1/6	2/6	1/6	1/6

Since the mean of all sample means () is population mean so sample mean is considered for making inference on population mean which is unknown.