To find Alan's average course grade, we use the weighted mean formula:

$\text{Weighted Mean} = \frac{\sum (w_i \cdot x_i)}{\sum w_i}$

Where:

• $w_i$ = weight of each component (as a percentage, expressed as a decimal).
• $x_i$ = Alan's score in each component.

Step 1: Break down the problem

• Weights:

  • Each test: $15\% = 0.15$
  • Term paper: $20\% = 0.20$
  • Final exam: $20\% = 0.20$

• Scores:

  • Tests: $78, 92, 82, 80$
  • Term paper: $86$
  • Final exam: $90$

Step 2: Calculate the weighted contributions

For each component, compute $w_i \cdot x_i$:

1. Tests:

   = 11.7 + 13.8 + 12.3 + 12.0 = 49.8$$

2. Term paper: $0.20 \cdot 86 = 17.2$

3. Final exam: $0.20 \cdot 90 = 18.0$

Step 3: Sum the weighted contributions

$49.8 + 17.2 + 18.0 = 85.0$

Step 4: Verify the total weight

The total weight is: $0.15 + 0.15 + 0.15 + 0.15 + 0.20 + 0.20 = 1.00$

Step 5: Compute the final weighted mean

Since the total weight is 1.00, the weighted mean is: $85.0$

Final Answer:

Alan's average course grade is 85.0.

Would you like more details or have any questions? 😊

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Expanding Questions:

1. What is the significance of the weighted mean in grading systems?
2. How would Alan’s grade change if he scored 95 on the final exam?
3. If the term paper's weight were reduced to 15%, how would it affect his average?
4. Can you derive the same result using Excel or another computational tool?
5. How does weighting reflect the importance of different components in overall performance?

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Tip:

Always double-check weights add up to 100% (or 1.0) when using the weighted mean formula!