Answer to Question #316850 in Statistics and Probability for Suu

Question

 In a university of 100 men and 50 ladies the professor noted the number of days absent from class during the period of the four years of the programme. For the men, the average number of absences was 15 with a standard deviation of 7, and for the ladies the average number of absences was 10 with a standard deviation of 6. What are the mean and the standard deviation of the absences for the entire class of students?

Answer 1

$\sigma^2=\frac{(n_1-1)\sigma_1^2+(n_2-1)\sigma_2^2}{n_1+n_2-2}=\frac{99\times 49+49\times36}{100+50-2}=44.7$

$\mu=\frac{\mu_1n_1+\mu_2n_2}{n_1+n_2}=\frac{100\times15+50\times10}{100+50}=13.3$

$\sigma= \sqrt{\sigma^2}=6.7$