Question

There are three students (Alice, Bill and Roby) applying the scholarships which are evaluated by four professors. Each professor (P1, P2, P3 and P4) gives a score (between 0 and 10) which is then combined into an overall score for each student.
Here are the scores given by the four professors:
P1 gives 8, 6, 3 to Alice, Bill and Roby, respectively;
P2 gives 7, 6, 3 to Alice, Bill and Roby, respectively;
P3 gives 6, 4, 7 to Alice, Bill and Roby, respectively;
P4 gives 4, 9, 7 to Alice, Bill and Roby, respectively.
(1) If each judge's score has equal importance, which student(s) get(s) the highest overall score based on the arithmetic mean?
(2) If the importance for the four professors P1, P2, P3 and P4 are 0.4, 0.3, 0.2 and 0.1, respectively. Which student(s) get(s) the highest overall weighted score based on the weighted arithmetic mean?
(3) If using Borda count, such that a student awards 3 points for first place, 1 point for second place and 0 points for third place, what are the overall scores for the three students?

Answer 1

Answer:-

Given That:-

There are three students (Alice, Bill and Roby) applying the scholarships which are evaluated by four professors. Each professor (P1, P2, P3 and P4) gives a score (between 0 and 10) which is then combined into an overall score for each student.

(1) If each judge's score has equal importance, which student(s) get(s) the highest overall score based on the arithmetic mean?

The simple arithmetic mean scores.

	Alice	Bill	Roby
P1	8	6	3
P2	7	6	3
P3	6	4	7
P4	4	9	7
Total Score	6.25	6.25	5

Both Alice and Bill get highest average score.

(2) If the importance for the four professors P1, P2, P3 and P4 are 0.4, 0.3, 0.2 and 0.1, respectively. Which student(s) get(s) the highest overall weighted score based on the weighted arithmetic mean?

Weighted Average Score

Weights		Alice	Bill	Roby
0.4	P1	8	6	3
0.3	P2	7	6	3
0.2	P3	6	4	7
0.1	P4	4	9	7
	Total Score	6.9	5.9	4.2

Alice gets the highest overall weighted score.

(3) If using Borda count, such that a student awards 3 points for first place, 1 point for second place and 0 points for third place, what are the overall scores for the three students?

Borda Value Score:

	Alice	Bill	Roby
P1	8	6	3
P2	7	6	3
P3	6	4	7
P4	4	9	7
Borda Count Scores
	Alice	Bill	Roby
P1	3	1	0
P2	3	1	0
P3	1	0	3
P4	0	3	1
Total Score	1.75	1.25	1

Alice gets the highest overall score.

Thank you for your supporting. Please upvote my answer...