Overview
This lecture covers how to calculate weighted averages for course grades using different scoring scenarios and demonstrates how to determine the minimum score needed on a final exam to reach desired overall grades.
Scenario 1: Calculating Overall Course Grade
- The syllabus weights: Homework 10%, Quizzes 20%, each of 3 Exams 15%, Final 25%.
- Convert each earned score to a decimal by dividing by 100.
- Multiply each section’s decimal score by its weight to get each category’s contribution.
- Homework: 100% gives 1 × 10% = 10%.
- Quizzes: 89% gives 0.89 × 20% = 17.8%.
- Exam 1: 90% gives 0.90 × 15% = 13.5%.
- Exam 2: 85% gives 0.85 × 15% = 12.75%.
- Exam 3: 97% gives 0.97 × 15% = 14.55%.
- Final: 70% gives 0.70 × 25% = 17.5%.
- Add all category contributions: total is 85.8%, rounded to 86%.
Scenario 2: Calculating Needed Final Exam Score
- Syllabus weights: Homework 15%, Quizzes 5%, Exams 1–3: 15%, 17%, 18%, Final 30%.
- Scores received: Homework 90%, Quizzes 100%, Exam 1 85%, Exam 2 90%, Exam 3 93%.
- Convert and multiply: Homework 0.90 × 15% = 13.5%; Quizzes 1 × 5% = 5%; Exam 1 0.85 × 15% = 12.75%; Exam 2 0.90 × 17% = 15.3%; Exam 3 0.93 × 18% = 16.74%.
- Partial total (excluding final): 63.29% after 70% of coursework.
- Current average: 63.29 ÷ 70% = 90%.
- To achieve a specific final grade, set up equation: 63.2 + 30x = desired percent.
- For 93% (A): 30x = 29.8 → x = 0.99 → 99% needed.
- For 85% (B): 30x = 21.8 → x = 0.73 → 73% needed.
- For 75% (C): 30x = 11.8 → x = 0.39 → 39% needed.
Key Terms & Definitions
- Weighted Average — An average where each component contributes a specified percentage to the total.
- Decimal Conversion — Dividing a percentage score by 100 to use in calculations.
- Category Contribution — The product of a section’s decimal score and its weight.
Action Items / Next Steps
- Practice calculating weighted averages for your own course syllabi.
- Complete any assigned homework using the weighted average formulas.