Question

A population consists of the following five values: 1, 3, 4, 4, and 6. List all samples of size 2 from left to right without replacement, and compute the mean of each sample. (Round your mean value to 1 decimal place.)

Answer 1

Answer:

The sample of sizes 2 and their mean are given below.

Step-by-step explanation:

The population consist of  5 values, S = {1, 3, 4, 4, 6}.

The number of samples of size 2 (without replacement) that can be formed from these 5 values is:

${5\choose 2}=\frac{5!}{2!(5-2)!} =10$

Th formula to compute the mean is:

$\bar x=\frac{1}{n}\sum x_{i}$

List the 10 samples and their mean as follows:

Sample                       Mean

(1, 3)                    $\bar x=\frac{1}{2}[1+3]=\frac{4}{2}=2.0$

(1, 4)                    $\bar x=\frac{1}{2}[1+4]=\frac{5}{2}=2.5$

(1, 4)                    $\bar x=\frac{1}{2}[1+4]=\frac{5}{2}=2.5$

(1, 6)                    $\bar x=\frac{1}{2}[1+6]=\frac{7}{2}=3.5$

(3, 4)                   $\bar x=\frac{1}{2}[3+4]=\frac{7}{2}=3.5$

(3, 4)                   $\bar x=\frac{1}{2}[3+4]=\frac{7}{2}=3.5$

(3, 6)                   $\bar x=\frac{1}{2}[3+6]=\frac{9}{2}=4.5$

(4, 4)                   $\bar x=\frac{1}{2}[4+4]=\frac{8}{2}=4.0$

(4, 6)                   $\bar x=\frac{1}{2}[4+6]=\frac{10}{2}=5.0$

(4, 6)                   $\bar x=\frac{1}{2}[4+6]=\frac{10}{2}=5.0$