The alumni club of Jefferson College gives a $10,000 award to the most outstandi
ID: 3245831 • Letter: T
Question
The alumni club of Jefferson College gives a $10,000 award to the most outstanding athlete each year. Since competitive sports include football, basketball, swimming, and tennis, the rating scale is a way of comparing athletes who participate in any of the sports. Each candidate is rated on a scale of 1 to 10 (with 10 being the best) for individual performance, win–loss record of team, grade point average, and sportsmanship. The ratings are then averaged using a weight of 5 for individual performance, 2 for win–loss record of team, 1 for grade point average, and 3 for sportsmanship.
a.One athlete had the following ratings: 9 for individual performance, 7 for team record, 6 for grade point average, and 8 for sportsmanship. Compute the weighted average of the ratings.
b. Another athlete had ratings of 8 for individual performance, 9 for team record, 5 for grade point average, and 9 for sportsmanship. Compute the weighted average of these ratings. Which athlete had the higher average rating?
Explanation / Answer
The weights of the different categories would be given by,
a.One athlete had the following ratings: 9 for individual performance, 7 for team record, 6 for grade point average, and 8 for sportsmanship. Compute the weighted average of the ratings.
Solution : The weighted average would be given by,
WA = (9*5+7*2+6*1+8*3)/(5+2+1+3) = 8.09
b. Another athlete had ratings of 8 for individual performance, 9 for team record, 5 for grade point average, and 9 for sportsmanship. Compute the weighted average of these ratings.
Solution : The weighted average for this athelete would be given by,
WA = (8*5+9*2+5*1+9*3)/(5+2+1+3) = 8.18
Which athlete had the higher average rating?
The weighted average rating of second athelete is higher .
Categories Weight Individual performance 5 Win loss record 2 Grade point average 1 Sportsmanship 3Related Questions
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