Refer to Problem 5.

a. Use the answer you obtained in Problem 5(b) and Definition 3.11 to find the mean of the variable x. Interpret your answer.

b. Can you obtain the mean of the variable x̅ without doing the calculation in part (a)? Explain your answer.

Problem 5(b)

Complete the second and third columns of the table.

Definition 3.11

For a variable x, the mean of all possible observations for the entire population  is called the population mean or mean of the variable x. It is denoted μx  or, when no confusion will arise, simply μ. For a finite population,

where N is the population size.

Sample A, B, C, D A, B, C, E A, B, C, F. A, B, D, E. A, B, D, F A, B, E, F. A, C, D, E A, C, D, F A, C, E, F A. D, E, F B, C, D, E C, D, F B, B, C, E, F B, D, E, F C, D, E, F Salaries 8, 12, 16, 20 8, 12, 16, 24 8, 12, 16, 28 8, 12, 20, 24 8, 12, 20, 28 8, 12, 24, 28 15 X 14 15 16 16 17 18