Question

What is the weighted average of four test scores of 60, 70, 80, and 90, with weights of 20%, 20%, 30%, and 30%?(1 point) Responses 77 77 75 75 81 81 73

Answer 1

To calculate the weighted average of the test scores, you can follow these steps:

1. Multiply each test score by its corresponding weight.
2. Add the weighted scores together.
3. Divide by the sum of the weights (which should equal 1 if they are expressed as percentages).

Here are the scores and their corresponding weights:

- Test score 1: 60, Weight: 20% (0.20)
- Test score 2: 70, Weight: 20% (0.20)
- Test score 3: 80, Weight: 30% (0.30)
- Test score 4: 90, Weight: 30% (0.30)

Now, calculate the weighted scores:

- Weighted score 1: \(60 \times 0.20 = 12\)
- Weighted score 2: \(70 \times 0.20 = 14\)
- Weighted score 3: \(80 \times 0.30 = 24\)
- Weighted score 4: \(90 \times 0.30 = 27\)

Next, sum the weighted scores:

\[
12 + 14 + 24 + 27 = 77
\]

The sum of the weights is:

\[
0.20 + 0.20 + 0.30 + 0.30 = 1.00
\]

Finally, since the weights sum to 1, the weighted average score is:

\[
\text{Weighted Average} = 77
\]

Thus, the weighted average of the four test scores is **77**.