Question

In her first year of university, Mary recieved the following grades: 12, 7, 11, 11, 12, 11 Similarly in his first year, Bob recieved the following grades: 11, 11, 9, 11, 9, 8

(a)	Compute the population mean and variance for Mary's grades.

(b)	Compute the population mean and variance for Bob's grades.

Answer 1

Solution(a)
Given in the question
Mary received the following grades in her first year of university
12,7,11,11,12,11
So population mean can be calculated as
Population mean (mary) = Xi/n = (12+7+11+11+12+11)/6= 64/6 = 10.67
Population variance can be calculated as
Population variance(^2) = (Xi-mary)^2 /n = ((12-10.67)^2 + (7-10.67)^2 + (11-10.67)^2 + (11-10.67)^2 + (12-10.67)^2 + (11-10.67)^2)/6 = 17.33/6 = 2.89
Solution(b)
Given in the question
Bob received the following grades in her first year of university
11,11,9,11,9,8
So population mean can be calculated as
Population mean (Bob) = Xi/n = (11+11+9+11+9+8)/6= 58/6 = 9.83
Population variance can be calculated as
Population variance(^2) = (Xi-Bob)^2 /n = ((11-9.83)^2 + (11-9.83)^2 + (9-9.83)^2 + (11-9.83)^2 + (9-9.83)^2 + (8-9.83)^2)/6 = 8.83/6 = 1.47