To find the weighted average, we use the formula:

$\text{Weighted Average} = (\text{Weight of Tests} \times \text{Average of Test Scores}) + (\text{Weight of Quizzes} \times \text{Average of Quiz Scores}) + (\text{Weight of Projects} \times \text{Average of Project Scores})$

Step 1: Calculate the averages for each category.

• Test Scores: 92, 87, 67, 92, 95 $\text{Average of Tests} = \frac{92 + 87 + 67 + 92 + 95}{5} = \frac{433}{5} = 86.6$

• Quiz Scores: 75, 89, 100 $\text{Average of Quizzes} = \frac{75 + 89 + 100}{3} = \frac{264}{3} = 88$

• Project Scores: 100, 85, 95 $\text{Average of Projects} = \frac{100 + 85 + 95}{3} = \frac{280}{3} = 93.33$

Step 2: Apply the weights.

• Weight of Tests: 50% or 0.50
• Weight of Quizzes: 30% or 0.30
• Weight of Projects: 20% or 0.20

Now calculate the weighted average: $\text{Weighted Average} = (0.50 \times 86.6) + (0.30 \times 88) + (0.20 \times 93.33)$ $= 43.3 + 26.4 + 18.666 = 88.366$

Final Result:

The weighted average is approximately 88.37.

Would you like further details or explanations?

Here are 5 related questions:

1. How would the weighted average change if the project weight was 25%?
2. What happens if one of the test scores is significantly lower than the others?
3. How do you calculate the median of the test scores instead of the average?
4. Can you explain how changing the weights impacts the final weighted average?
5. What is the difference between weighted and unweighted averages?

Tip: When calculating a weighted average, make sure the sum of all weights equals 100% (or 1 when expressed as decimals).