Question

A group of students got the following scores in a test:6,9,12,15,18 and 21. Consider samples of size 3thag can be drawn from this population. List all the possible samples and the corresponding mean.

Answer 1

The number of possible samples of size $n=3$ from a population of size $N=6$ is,

$\binom{6}{3}=20$

The sample means are derived from the formula, $\bar x_i={\sum x_i\over3}$

The list below gives the possible samples with their corresponding means.

Sample mean

(6,9,12) 9

(6,9,15) 10

(6,9,18) 11

(6,9,21) 12

(6,12,15) 11

(6,12,18) 12

(6,12,21) 13

(6,15,18) 13

(6,15,21) 14

(6,18,21) 15

(9,12,15) 12

(9,12,18) 13

(9,12,21) 14

(9,15,18) 14

(9,15,21) 15

(9,18,21) 16

(12,15,18) 15

(12,15,21) 16

(12,18,21) 17

(15,18,21) 18