Answer to Question #349487 in Statistics and Probability for Iyot

Question

The numbers of workers of a new fast food restaurant with seven outlets are 9 10 9 11 13 12 and 8 compute the population mean population variance and population standard deviation use the long method

Answer 1

We have population values 9,10,9,11,13,12,8, population size N=7.

Mean of population $(\mu)$ = $\dfrac{9+10+9+11+13+12+8}{7}=\dfrac{72}{7}$

Variance of population 

$$\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}=\dfrac{1}{343}(81+4+81+25$$ $$+361+144+256)=\dfrac{136}{49}$$ $$\sigma=\sqrt{\sigma^2}=\sqrt{\dfrac{136}{49}}=\dfrac{2\sqrt{34}}{7}\approx1.666$$