Answer to Question #318877 in Statistics and Probability for Ali De Austria

Question

A finite population consists of 5 elements. 10, 12, 14, 16, 15. Consider the sample of size 3 that can be drawn from this population.

What is N?

What is the mean of the population?

What is the variance of the population?

What is the standard deviation of the population?

How many samples can be drawn in the population?

What is the mean of the sample?

What is the variance of the sample?

What is the standard deviation of the sample?

Answer 1

What is N?

$=5$

What is the mean of the population?

$=\frac{10+12+14+16+15}{5}=\frac{67}{5}=13.4$

What is the variance of the population?

$=\frac{(10-13.4)^2+(12-13.4)^2+(14-13.4)^2+(16-13.4)^2+(15-13.4)^2}{5}=\frac{23.2}{5}=4.64$

What is the standard deviation of the population?

$=\sqrt{4.64}=2.154$

How many samples can be drawn in the population?

$C(5,3)=10$

What is the mean of the sample?

Mean $=13.4$

What is the variance of the sample?

$=180.33334-13.4^2=0.7734$

What is the standard deviation of the sample?

$=\sqrt{0.7734}=0.8794$