Question

A population consists of the five numbers: 1, 3, 5, 7, and 9.

Consider samples of size 3 that can be drawn from this population

2 points for every Sample and 1 point for the corresponding Mean of that Sample

Answer 1

1, 3, 5, 7, and 9.

There are totally ${5 \choose 3} =10$ samples of size 3 can be drawn from this population

Here they are: (1, 3, 5), (1, 3, 7), (1, 3, 9), (1, 5, 7), (1, 5, 9), (1, 7, 9), (3, 5, 7), (3, 5, 9), (3, 7, 9), (5, 7, 9)

The mean of the sample is the sum of it's elements divided by amount of them. So,

$S{\scriptscriptstyle 1}=4.5$

$S{\scriptscriptstyle 2}=5.5$

$S{\scriptscriptstyle 3}=6.5$

$S{\scriptscriptstyle 4}=6.5$

$S{\scriptscriptstyle 5}=7.5$

$S{\scriptscriptstyle 6}=8.5$

$S{\scriptscriptstyle 7}=7.5$

$S{\scriptscriptstyle 8}=8.5$

$S{\scriptscriptstyle 9}=9.5$

$S{\scriptscriptstyle 10}=10.5$

The corresponding mean is ${\frac {S{\scriptscriptstyle 1} +...+ S{\scriptscriptstyle 10}} {10}}= 7.5$