Answer to Question #311330 in Statistics and Probability for Jessa

Question

Consider a population consisting the scores of 6 students in a statistic test 18, 22, 25, 28, 32, 36

List the possible samples and the corresponding means in the table

Answer 1

* The question is not complete and includes; suppose sample sizes of 3 are drawn from this population.

Solution

Population size $N=6$

Sample size $n=3$

Possible number of samples

$=C_6^3= \binom{6}{3}=20$ samples

The samples and their corresponding means

$\def\arraystretch{1.5}\begin{array}{c:c:c}no &Sample& Sample mean\\\hline1&18,22,25&21.67\\\hdashline2&18,22,28&22.67\\\hdashline3&18,22,32&24.00\\\hdashline4&18,22,36&25.33\\\hdashline5&18,25,28&23.67\\\hdashline6&18,25,32&25.00\\\hdashline7&18,25,36&26.33\\\hdashline8&18,28,32&26.00\\\hdashline9&18,28,36&27.33\\\hdashline10&18,32,36&28.67\\\hdashline11&22,25,28&25.00\\\hdashline12&22,25,32&26.33\\\hdashline13&22,25,36&27.67\\\hdashline14&22,28,32&27.33\\\hdashline15&22,28,36&28.67\\\hdashline16&22,32,36&30.00\\\hdashline17&25,28,32&28.33\\\hdashline18&25,28,36&29.67\\\hdashline19&25,32,36&31.00\\\hdashline20&28,32,36&32.00\\\hline\end{array}$