A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 60, 80, and 89. Sara's quiz scores are 85, 94, 83, and 84. Her final examination score is 60. Use the weighted mean formula to find Sara's average for the course. (Round your answer to one decimal place.)
To find Sara's average for the course using the weighted mean formula, you first need to determine the weights for each component of the course (tests, quizzes, and final examination).
In this case, each test counts as two quizzes and the final examination counts as two tests. Therefore, the weights for the tests would be 2, the weights for the quizzes would be 1, and the weight for the final examination would also be 2.
Next, you can calculate the weighted score for each component by multiplying the actual score by its weight.
For the tests:
Weighted score for the first test = 60 * 2 = 120
Weighted score for the second test = 80 * 2 = 160
Weighted score for the third test = 89 * 2 = 178
For the quizzes:
Weighted score for the first quiz = 85 * 1 = 85
Weighted score for the second quiz = 94 * 1 = 94
Weighted score for the third quiz = 83 * 1 = 83
Weighted score for the fourth quiz = 84 * 1 = 84
For the final examination:
Weighted score for the final examination = 60 * 2 = 120
Now you can calculate the sum of all the weighted scores:
Sum of the weighted scores = 120 + 160 + 178 + 85 + 94 + 83 + 84 + 120 = 924
Finally, to find Sara's average for the course, divide the sum of the weighted scores by the total weight:
Average = Sum of the weighted scores / Total weight
Average = 924 / (2 + 2 + 1 + 1 + 1 + 1 + 1 + 1) = 924 / 10 = 92.4
Therefore, Sara's average for the course is 92.4.