Answer to Question #327332 in Statistics and Probability for raymond relao

Question

A group of students got the following scores in an achievement test: 9,12,15,18, 21, and 24. Consider samples of size 3 that can be drawn from this population. A. Determine and list all possible samples and the corresponding sample means. SAMPLE MEANS RANDOM SAMPLES​

Answer 1

The number of possible samples which can be selected without replacement is

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! }=\cfrac{6! } {3! \cdot3! }=20.$

$\textnormal{Sample\qquad\qquad Mean}\\ \ \\ 9,12,15\qquad \cfrac{9+12+15}{3}=12\\ 9,12,18\qquad \cfrac{9+12+18}{3}=13\\ 9,12,21\qquad \cfrac{9+12+21}{3}=14\\ 9,12,24\qquad \qquad 15\\ 9,15,18\qquad \qquad 14\\ 9,15,21\qquad \qquad 15\\ 9,15,24\qquad \qquad 16\\ 9,18,21\qquad \qquad 16\\ 9,18,24\qquad \qquad 17\\ 9,21,24\qquad \qquad 18\\ 12,15,18\qquad \qquad 15\\ 12,15,21\qquad \qquad 16\\ 12,15,24\qquad \qquad 17\\ 12,18,21\qquad \qquad 17\\ 12,18,24\qquad \qquad 18\\ 12,21,24\qquad \qquad 19\\ 15,18,21\qquad \qquad 18\\ 15,18,24\qquad \qquad 19\\ 15,21,24\qquad \qquad 20\\ 18,21,24\qquad \qquad 21.$