Question

solve for the mean, variance, and standard deviation of the given set of data of a population.

Answer 1

We have population values 8, 10, 12, 14, 16 and 18

Mean and Standard Deviation and Variance of population is computed as follows:

1.) Mean= $\mu = \frac{{\sum X}}{N}$ =$\frac{8+ 10,+12+ 14+16 +18}{6}=13$

2.) Standard Deviation $\sigma = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \mu)^2} {n}}$ =

$\sigma = \sqrt{\frac{(8-13)^2+(10-13)^2+(12-13)^2+(14-13)^2+(16-13)^2+(18-13)^2} {6}}$ =$\sqrt{\frac{70}{6}}=\sqrt{11.667}=3.42$

3.) Variance= $sd^2= 3.42^2= 11.67$

$\implies \dfrac{\sigma }{{\sqrt n }}\sqrt {\dfrac{{N – n}}{{N – 1}}} = \dfrac{{3.42}}{{\sqrt 3 }}\sqrt {\dfrac{{6 – 3}}{{6 – 1}}} = 1.529$ .