A group of students got the following scores in a test:9,12,15,18,21 and 24. Consider samples of size 3thag can be drawn from this population. construct a sampling distribution of the resulting sample means

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

(9,12,15) 12

(9,12,18) 13

(9,12,21) 14

(9,12,24) 15

(9,15,18) 14

(9,15,21) 15

(9,15,24) 16

(9,18,21) 16

(9,18,24) 17

(9,21,24) 18

(12,15,18) 15

(12,15,21) 16

(12,15,24) 17

(12,18,21) 17

(12,18,24) 18

(12,21,24) 19

(15,18,21) 18

(15,18,24) 19

(15,21,24) 20

(18,21,24) 21

The sampling distribution is,

$\bar x_i$ 12 13 14 15 16 17 18 19 20 21

$p(\bar x_i)$ ${1\over20}$ ${1\over20}$ ${1\over10}$ ${3\over20}$ ${3\over20}$ ${3\over20}$ ${3\over20}$ ${1\over10}$ ${1\over20}$ ${1\over20}$