Question

A population consists of four numbers 3, 7, 11, 15. consider all possible sample size 2 which can be drawn without replacement. Find mean and SD in the population.

Answer 1

$Number = \frac{N!}{n!(N-n)!} \\ = \frac{4!}{2!(4-2)!} \\ = \frac{3 \times 4}{2} \\ = 6$

Samples:

3,7

3,11

3,15

7,11

7,15

11,15

$Mean = \frac{3+7+11+15}{4} = 9 \\ SD = \sqrt{\frac{1}{4-1}( (3-9)^2+(7-9)^2 +(11-9)^2 + (15-9)^2 )} \\ = \sqrt{ \frac{1}{3}(36+4+4+36) } \\ = 5.164$