Question

Find the weighted average.

Weighting: 50% Tests, 30% quizzes, 20% projects

Scores are percents

Tests Quizzes Projects
92 75 100
87 89 85
67 100 92.5
92
95

What the weighted average:​

Answer 1

To calculate the weighted average, you need to multiply each score by its corresponding weight and then sum up these products.

Weighted average = (0.50 * Average of Tests) + (0.30 * Average of Quizzes) + (0.20 * Average of Projects)

Average of Tests = (92 + 87 + 67 + 92 + 95) / 5 = 86.6

Average of Quizzes = (75 + 89 + 100 + 100) / 4 = 91

Average of Projects = (100 + 85 + 92.5) / 3 = 92.5

Now, plug these values into the formula:

Weighted average = (0.50 * 86.6) + (0.30 * 91) + (0.20 * 92.5)

Weighted average = 43.3 + 27.3 + 18.5

Weighted average = 89.1

So, the weighted average is 89.1.

Answer 2

Based on the given weight for tests, quizzes and projects, the weighted average is 313.8.

How to find the weighted average

To find the weighted average, multiply each score by its corresponding weight, sum up those products, and divide by the total weight.

Given:

Weights:

Tests: 50%

Quizzes: 30%

Projects: 20%

Scores:

Tests: 92, 87, 67

Quizzes: 75, 89, 100, 92, 95

Projects: 100, 85, 92.5

Let's calculate the weighted average:

Step 1: Calculate the weighted sum for each category.

Tests weighted sum = (92 * 0.5) + (87 * 0.5) + (67 * 0.5)

= 46 + 43.5 + 33.5

= 123

Quizzes weighted sum = (75 * 0.3) + (89 * 0.3) + (100 * 0.3) + (92 * 0.3) + (95 * 0.3)

= 22.5 + 26.7 + 30 + 27.6 + 28.5

= 135.3

Projects weighted sum = (100 * 0.2) + (85 * 0.2) + (92.5 * 0.2)

= 20 + 17 + 18.5

= 55.5

Step 2: Calculate the total weighted sum.

Total weighted sum = Tests weighted sum + Quizzes weighted sum + Projects weighted sum

= 123 + 135.3 + 55.5

= 313.8

Step 3: Calculate the total weight.

Total weight = Weight of Tests + Weight of Quizzes + Weight of Projects

= 0.5 + 0.3 + 0.2

= 1

Step 4: Calculate the weighted average.

Weighted average = Total weighted sum / Total weight

= 313.8 / 1

= 313.8

Therefore, the weighted average is 313.8.