Fifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam?
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A. B. C. D. E.E
(15*90)+(7*85)+(10*93) = 2875. Therefore, the weighted mean will be 2875/32 = 89.84.
To find the weighted mean for the 32 students taking the exam, we need to consider the average grades of each group of students and their respective weights.
Given information:
The weighted mean formula is calculated by multiplying each average grade by its respective weight, summing up the products, and dividing by the total number of students.
Let's calculate the weighted mean step by step:
Step 1: Calculate the total weight. The total weight is the sum of the individual weights for each group of students. Since the number of students in each group is not given, we can assume that each group has the same number of students. Therefore, the total weight is the sum of the number of students in each group:
Total weight = 15 (accounting majors) + 7 (marketing majors) + 10 (finance majors) = 32
Step 2: Calculate the weighted sum. The weighted sum is the sum of the products obtained by multiplying the average grade of each group by its weight. Let's calculate it for each group:
Weighted sum for accounting majors = Average grade * Number of students = 90 * 15 = 1350 Weighted sum for marketing majors = Average grade * Number of students = 85 * 7 = 595 Weighted sum for finance majors = Average grade * Number of students = 93 * 10 = 930
Step 3: Calculate the weighted mean. The weighted mean is obtained by dividing the weighted sum by the total weight:
Weighted mean = (Weighted sum for accounting + Weighted sum for marketing + Weighted sum for finance) / Total weight = (1350 + 595 + 930) / 32 = 2875 / 32 ≈ 89.84
Therefore, the weighted mean for the 32 students taking the exam is approximately 89.84.
The correct answer is E. 89.84.