A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 94, 78, 80, and 88. Alan received an 84 on his term paper. His final examination score was 90. Use the weighted mean formula to find Alan's average for the course. (Round your answer to one decimal place.)
Question
A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 94, 78, 80, and 88. Alan received an 84 on his term paper. His final examination score was 90. Use the weighted mean formula to find Alan's average for the course. (Round your answer to one decimal place.)
Solution
To calculate Alan's average for the course, we need to use the weighted mean formula. The weighted mean is calculated by multiplying each value by its corresponding weight and then summing those results. The weights in this case are the percentages each component contributes to the final grade.
Here are the steps:
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Multiply each test score by its weight (15% or 0.15):
- 94 * 0.15 = 14.1
- 78 * 0.15 = 11.7
- 80 * 0.15 = 12
- 88 * 0.15 = 13.2
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Multiply the term paper score by its weight (20% or 0.20):
- 84 * 0.20 = 16.8
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Multiply the final exam score by its weight (20% or 0.20):
- 90 * 0.20 = 18
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Add all these values together to get the weighted mean:
- 14.1 + 11.7 + 12 + 13.2 + 16.8 + 18 = 85.8
So, Alan's average for the course is 85.8 (rounded to one decimal place).
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