Quiz Scores, a Dropped Score, and the Cost of Paperwork
Devon's syllabus weights quizzes at 20%, unit tests at 50%, essays at 20%, and the final exam at 10%. His quiz scores are 92, 88, 90, 94, 45, and 91. The 45 came from a quiz he missed while hospitalized; the documented-absence policy allows dropping one lowest quiz score before averaging. His unit test average is 78 and his essay average is 85. The final exam has not been taken. Devon wants at least a B (80) in the course and is deciding whether to file the absence paperwork, which requires requesting a doctor's note.
1. Compute Devon's quiz average with and without the dropped score, and express the difference in course-grade points.
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Without the drop: 92 + 88 + 90 + 94 + 45 + 91 = 500; 500 ÷ 6 = 83.33
With the drop (45 removed): 92 + 88 + 90 + 94 + 91 = 455; 455 ÷ 5 = 91.00
Difference: 91.00 − 83.33 = 7.67 quiz points
Convert to course-grade points: the quiz category is worth 20%, so 7.67 × 0.20 = 1.53 points on the final course grade.
Sanity check on the arithmetic: a single score of 45 pulls the six-score mean down by roughly 7.7 points, which is why dropping it moves the average so much - one outlier out of six has heavy leverage. Had he taken twenty quizzes, the same 45 would have moved almost nothing.
2. Using the dropped-score average, what minimum final exam score does Devon need to reach 80?
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Work backward from the categories already earned.
- Quizzes: 91.00 × 0.20 = 18.20
- Unit tests: 78 × 0.50 = 39.00
- Essays: 85 × 0.20 = 17.00
- Subtotal: 18.20 + 39.00 + 17.00 = 74.20 out of the 90 points available before the final
Set up the requirement: 74.20 + 0.10F = 80
0.10F = 5.80
F = 58
Check: 74.20 + 5.80 = 80.00. Devon needs a 58 on the final - comfortably below his other scores, so a B is likely as long as he does not shut down on the exam.
3. Compute the final-exam score needed if he does not file the paperwork, and use the comparison to advise him.
Read the worked answer
Without the drop: quizzes 83.33 × 0.20 = 16.67
- Subtotal: 16.67 + 39.00 + 17.00 = 72.67
Requirement: 72.67 + 0.10F = 80 → 0.10F = 7.33 → F = 73.3
Comparison: filing the paperwork lowers the required final score from about 73 to 58 - a 15-point swing. Put differently, the drop is worth 1.53 course points, and because the final is only 10% of the grade, each course point is worth ten final-exam points.
Advice: file it. The cost is one doctor's request; the benefit is a large cushion against a bad exam day. Note the leverage point, though: this is only true because the final is weighted so lightly. If the final were worth 30%, the same 1.53 points would be worth only about 5 points on the exam, and the paperwork would matter far less. The decision depends on the weighting, not on the size of the 45.