Question

Find the mean, variance and standard deviation of the following measures 2,5,6,3,9,10,12

Answer 1

We have population values 2,5,6,3,9,10,12, population size N=7.

Mean of population $(\mu)$ = $\dfrac{2+5+6+3+9+10+12}{7}=\dfrac{47}{7}$

Variance of population 

$$\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}=\dfrac{1}{7}(\dfrac{1089}{49}+\dfrac{144}{49}+\dfrac{25}{49}$$

$$+\dfrac{676}{49}+\dfrac{256}{49}+\dfrac{529}{49}+\dfrac{1369}{49})=\dfrac{584}{49}\approx11.918367$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{\dfrac{584}{49}}=\dfrac{2\sqrt{146}}{7}\approx3.4523$$