Question

A population consists of the numbers 2, 4, 5, 9, 10. List all possible sample size of 3 from this population without replacement and determine the mean of each sample.

Answer 1

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

$\begin{pmatrix} N \\ n \end{pmatrix}=\cfrac{N! } {n! \cdot(N-n)! }=\cfrac{5! } {3! \cdot2! }=10.$

$\textnormal{Sample\qquad\qquad Mean}\\ \ \\ 2,4,5\qquad \cfrac{2+4+5}{3}=3\cfrac23\\ 2,4,9\qquad \cfrac{2+4+9}{3}=5\\ 2,4,10\qquad \cfrac{2+4+10}{3}=5\cfrac13\\ 2,5,9\qquad \cfrac{2+5+9}{3}=5\cfrac13\\ 2,5,10\qquad \cfrac{2+5+10}{3}=5\cfrac23\\ 2,9,10\qquad \cfrac{2+9+10}{3}=7\\ 4,5,9\qquad \cfrac{4+5+9}{3}=6\\ 4,5,10\qquad \cfrac{4+5+10}{3}=6\cfrac13\\ 4,9,10\qquad \cfrac{4+9+10}{3}=7\cfrac23\\ 5,9,10\qquad \cfrac{5+9+10}{3}=8$