Answer to Question #319353 in Statistics and Probability for Wyne

Question

Consider a population consisting the scores of 6 students in a Statistic Test.

18, 22, 25, 28, 32, 36

Suppose samples of size 3 are drawn from this population, describe the sampling

distribution of the sample means following the steps below.

Step 4: List all possible

samples and their

corresponding means.

Answer 1

$\textnormal{Sample\qquad\qquad Mean}\\ \ \\ 18,22,25\qquad \cfrac{18+22+25}{3}=21\frac{2}{3}\\ 18,22,28\qquad \cfrac{18+22+28}{3}=22\frac{2}{3}\\ 18,22,32\qquad \cfrac{18+22+32}{3}=24\\ 18,22,36\qquad \qquad 25\frac{1}{3}\\ 18,25,28\qquad \qquad 23\frac{2}{3}\\ 18,25,32\qquad \qquad 25\\ 18,25,36\qquad \qquad 26\frac{1}{3}\\ 18,28,32\qquad \qquad 26\\ 18,28,36\qquad \qquad 27\frac{1}{3}\\ 18,32,36\qquad \qquad 28\frac{2}{3}\\ 22,25,28\qquad \qquad 25\\ 22,25,32\qquad \qquad 26\frac{1}{3}\\ 22,25,36\qquad \qquad 27\frac{2}{3}\\ 22,28,32\qquad \qquad 27\frac{1}{3}\\ 22,28,36\qquad \qquad 28\frac{2}{3}\\ 22,32,36\qquad \qquad 30\\ 25,28,32\qquad \qquad 28\frac{1}{3}\\ 25,28,36\qquad \qquad 29\frac{2}{3}\\ 25,32,36\qquad \qquad 31\\ 28,32,36\qquad \qquad 32.$