Answer to Question #196656 in Statistics and Probability for harshik

Question #196656

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.


1
Expert's answer
2021-05-23T15:21:15-0400

Number=N!n!(Nn)!=4!2!(42)!=3×42=6Number = \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=3+7+11+154=9SD=141((39)2+(79)2+(119)2+(159)2)=13(36+4+4+36)=5.164Mean = \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


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