Answer to Question #308796 in Statistics and Probability for Jmar

Question

a population consists of the five measurements 2, 6, 8, 3 & 1. how many different samples of size n=2 can be drawn from the population? what is the mean & variance of the sampling distribution of the sample means

Answer 1

we define the following

The number of possible samples = (5C2) =10 possible samples

possible samples and their mean are as below

(2,3) = 2.5

(2,8) = 5

(2,6) = 4

(2,1) = 1.5

(6,8) = 7

(6,3) = 4.5

(6,1) = 3.5

(8,3) = 5.5

(8,1) = 4.5

(3,1) = 2

hence the mean of the sample means = (2.5+5+4+1.5+7+4.5+3.5+5.5+4.5+2)/10

on solving we get it equals to 4 which is the solution.

variance = ( (2.5²+5²+4²+1.5²+7²+4.5²+3.5²+5.5²+4.5²+2²)/10 ) - (4²)

= 18.55 - 16 = 2.55