Answer to Question #313415 in Statistics and Probability for Darren

Question

Given the population 3 5 8 9 and 10. Suppose samples of size 3 are drawn from this population

Answer 1

Population size $N=5$

Sample size $n=3$

mean

$\mu=\dfrac{\sum_{i=1}^{i=N} X_i}{N}$

$\mu =\dfrac{3+5+8+9+10}{5}$

$\mu=7.0$

Standard deviation

$\sigma=\sqrt {\dfrac {\sum (X-\bar X)^2}n}$

$\sigma=\sqrt \frac{{(3-7)^2+(5-7)^2+(8-7)^2+(9-7)^2+(10-7)^2}}5$

$\sigma=\sqrt {\dfrac{16+4+1+4+9}5}$

$\sigma=2.61$