Weighted Average Calculator
Homework at 88 worth 15%, quizzes at 92 worth 10%, a midterm of 79 worth 25% and a final of 84 worth 50% give a weighted average of 84.15. The weighted average calculator puts the plain mean beside it and shows each value's share of the weight.
Weighted average
- Weighted average Sum of value x weight, divided by the total weight of 100.
- 84.15
- Plain mean of the values 1.6 higher than the weighted average, because it gives every value the same say.
- 85.75
- Count
- 4
- Total weight
- 100
| Value | Weight | Share of weight | Value x share |
|---|---|---|---|
| 88 | 15 | 15% | 13.2 |
| 92 | 10 | 10% | 9.2 |
| 79 | 25 | 25% | 19.75 |
| 84 | 50 | 50% | 42 |
| Total | 100 | 100% | 84.15 |
How the Average Calculator works
A weighted average, also called a weighted mean, gives some values more say than others. The formula for a weighted mean is the sum of each value times its weight, divided by the sum of the weights. For the default course grade that is (88 x 15 + 92 x 10 + 79 x 25 + 84 x 50) / (15 + 10 + 25 + 50) = (1,320 + 920 + 1,975 + 4,200) / 100 = 8,415 / 100 = 84.15. The plain mean of the same four scores is 343 / 4 = 85.75. The weighted figure is 1.6 lower because the two weakest scores, 79 and 84, carry 75% of the weight between them.
The weights are relative. The division by the total weight is what makes that true: 15, 10, 25, 50 and 0.15, 0.1, 0.25, 0.5 and 3, 2, 5, 10 all give 84.15. So the weights do not have to add up to 100.
A frequency table is a weighted average. When the weights are counts, the weighted average is the ordinary mean of the full list. Six students scoring 70, ten scoring 80 and four scoring 90 is 70:6, 80:10, 90:4, which gives (420 + 800 + 360) / 20 = 79, the same as the plain mean of all twenty scores.
The same formula, other names. A GPA is a weighted average of grade points with credit hours as the weights. The average price paid for shares bought in several lots is a weighted average of the prices with the number of shares as the weights. An average of percentages taken from groups of different sizes is a weighted average with the group sizes as the weights, which is why the plain mean of such percentages is usually wrong.
Each value's contribution. A value times its share of the total weight is its contribution. The contributions add up to the weighted average: 13.2 + 9.2 + 19.75 + 42 = 84.15. The final alone contributes 42 of the 84.15 points, half the grade, because it carries half the weight.
Average Calculator FAQ
What is the formula for a weighted average?
Weighted average = sum of (value x weight) / sum of weights. Scores of 88, 92, 79 and 84 weighted 15, 10, 25 and 50 give (1,320 + 920 + 1,975 + 4,200) / 100 = 84.15.
Do the weights have to add up to 100?
No. The formula divides by the total weight, so 15, 10, 25, 50 and 3, 2, 5, 10 give the same answer. Weights as percentages, decimals or counts all work.
How do I find a weighted average when some grades are missing?
Leave the missing items out, or give them a weight of zero, and the result is the weighted average of what has been graded. Do not enter a missing grade as a score of zero: 88:15, 92:10, 79:25 is 84.3, but adding 0:50 for an untaken final gives 42.15.
What is the difference between a weighted average and a simple average?
A simple average gives every value the same weight. A weighted average lets some values count more. They agree only when the weights are equal. With 88, 92, 79 and 84 the simple average is 85.75 and the weighted average at 15, 10, 25 and 50 is 84.15.