Why the weights change the result
A weighted average is the sum of (value × weight) divided by the sum of the weights. Take a quiz score of 90 worth 3 credits, a midterm of 84 worth 3 credits, and a final of 76 worth 4 credits. The products are 90 × 3 = 270, 84 × 3 = 252, and 76 × 4 = 304. The sum of the products is 270 + 252 + 304 = 826. The credits add to 3 + 3 + 4 = 10. The weighted average is 826 ÷ 10 = 82.6.
The plain mean of 90, 84, and 76 is 83.33, higher than 82.6, because that mean pretends the final counts the same as the quiz. It does not. The extra credit on the lower score is exactly what the weights are for. If every weight is 1, the weighted average and the ordinary average match.
Worked example, step by step
Weights do not have to be credits. They can be percentages that add to 100: homework 20%, quizzes 30%, final 50%. Then each score is multiplied by that percent and the products are added, which is the same formula because dividing by 100 at the end is already built into using weights that sum to 100. If your weights are 20, 30, and 50, the calculator divides by 100 for you. You do not also divide by 100 by hand.
- Write the three rows: 90 with weight 3, 84 with weight 3, 76 with weight 4.
- Multiply across: 270, 252, and 304.
- Add the products: 826. Add the weights: 10.
- Divide: 826 ÷ 10 = 82.6. On a 0–100 grade scale, that is the course average.
Bad weights
A negative weight reverses the meaning of that row and is rarely what a grade sheet intends. A weight of zero drops the row, which is correct if the assignment is excused. Leaving the weight blank drops the row too. The label column is only a reminder; it is not part of the math. Two rows can share a label.
Percent weights that sum to 90 or 110 are a common syllabus mistake. The calculator will still divide by whatever the weights add up to, so the result is a true weighted mean of the rows you typed. It will not silently force the weights to 100. If the syllabus is supposed to sum to 100, fix the weights before you trust the number.