Question

What is the sampling distribution of the sample mean? Provide examples.

 

Answer 1

 

When repeated samples of same size are taken from underlying population and calculate the sample mean of all samples then distribution of sample means are known as sampling distribution of sample mean.

Example:

Consider the population of four juvenile condors. Their weights in pounds are : 3, 4, 6, 11

This is the sampling distribution for samples of size 2:

Let X1 shows weight of first condor and X2 shows weight of second condor. List of all possibles different values of X1 and X2 and corresponding mean is as follows:

X1	X2	Sample mean
3	3	3
3	4	3.5
3	6	4.5
3	11	7
4	3	3.5
4	4	4
4	6	5
4	11	7.5
6	3	4.5
6	4	5
6	6	6
6	11	8.5
11	3	7
11	4	7.5
11	6	8.5
11	11	11
Total		96

So possible different values of is: 3, 3. 5, 4, 4.5, 5, 6, 7, 7.5, 8.5 ,11

There are 16 samples so probability of each sample is 1/16. Therefore sampling distribution of sample mean is:

Sample mean	P(sample mean)
3	0.0625
3.5	0.125
4	0.0625
4.5	0.125
5	0.125
6	0.0625
7	0.125
7.5	0.125
8.5	0.125
11	0.0625
Total	1