Question

Please show work - trying to understand how to do this so I can apply it to other problems.

Both Professor X and Professor Y agree that students who study for their examinations do better than those who do not. Both professors teach the same class, take a careful four level ranking of how hard their students studied and give a very similar examination.

This year the average score in Professor X’s class and the average score in Professor Y’s class by their level of study effort was virtually THE SAME:

Students who studied seriously scored an average of 100 points

Students who studied moderately earned an average of 80 points

Students who studies briefly earned an average of 60 points

Students who did not study earned an average of 40 points

Professor X                                                                               Professor Y

Class size   100                                                                         class size 100

20% of students Studied Seriously                                             40% of students studied seriously

           

40% of students studied moderately                                           40% of students studied moderately

30% of students studied briefly                                                  10% of students studies briefly

10% of students did not study at all                                            10% of students did not study at all

What is the average score in Professor X’s class? In Professor Y’s class?

What would be the average scores if both Professors had the SAME composition of students (in relation to the level of effort in studying)

Answer 1

the following table shows the different levels of effort, average scores for each level of effort and the proportion of students in who put in the efforts at each level in 2 classes

		Professor X	Professor Y
the level of effort in studying	Average score	Percentage of students	Percentage of students
Studied Seriously	100	20%	40%
studied moderately	80	40%	40%
studied briefly	60	30%	10%
did not study at all	40	10%	10%

The average score of any given class is

the average score in professor X's class is

the average score in professor Y's class is

If the composition of students, in relation to the level of effort in studying, is the same then the proportion of students in each effort level is 25% (There are 4 groups and hence the proportion of students at each level of effort is 1/4*100=25%

the average score if both Professors had the SAME composition of students

which is the average of 100,80,60, and 40 , that is (100+80+60+40)/4