Question

A sample of size 3 is taken from a population of the number of students in each class of Grade 9 students listed as 25, 30, 35, and 40.

Construct the sampling distribution of the sample means

Answer 1

Solution

Population size $N=4$

Sample size $n=3$

Possible samples

$=C_4^3= \binom{4}{3}=4$ samples

$\def\arraystretch{1.5}\begin{array}{c:c:c} no.& sample &mean\\\hline1.&25,30,35&30.00\\\hdashline2.&25,30,40&31.67\\\hdashline3.&25,35,40&33.33\\\hdashline4.&30,35,40&35.00\\\hline\end{array}$

Probability distribution

$\def\arraystretch{1.5}\begin{array}{c:c:c} mean&freq&prob\\\hline30.00&1&1/4\\\hdashline31.67&1&1/4\\\hdashline33.33&1&1/4\\\hdashline35.00&1&1/4\\\hline\end{array}$

Histogram