Question

Five people own and operate the Mona Bookstore in Vancouver. Each person is married, and the number of years each has been married is given below.

5 3 7 2 12

Suppose a random sample of three of the owners is selected. The sample statistic is the sample median M. Derive the sampling distribution of the statistic M. Calculate the mean and standard deviation of M.

Answer 1

Step 1:

Population: 5 3   7   2   12

Step 2:

Samples of size 3 and their median (M) are given by:

Sample	Median (M)
5   3    7	5
5   3    2	3
5   3    12	5
3    7     2	3
3    2 12	3
5    2     12	5
7   2     12	7
7     5    12	7
7     3      12	7
2 7      5	5

Step 3:

(i) Mean of M is given by:

(ii) Standard Deviation of M is given by