Question

Consider a population consisting of 3, 6, 7, 9, 10, 4, and 8. Suppose samples of size 2 are drawn from this population. Describe the sampling distribution of sample means. What is the population mean? 

Answer 1

The population mean is: $\mu=\frac{3+6+7+9+10+4+8}{7}\approx6.714$. All samples of size $2$ and their means are given in the table:

There are $21$ different samples of size 2.

The sampling distribution of sample means is given in the following table:

Thus, the sampling distribution of sampling means is given in the table above. The population mean is approximately equal to $6.714$.