Weighted Mean Calculator Formula
Understand the math behind the weighted mean calculator. Each variable explained with a worked example.
Formulas Used
Weighted Mean
weighted_mean = weighted_sum / weight_totalTotal Weight
total_weight = weight_totalVariables
| Variable | Description | Default |
|---|---|---|
v1 | Value 1 | 85 |
w1 | Weight 1 | 3 |
v2 | Value 2 | 90 |
w2 | Weight 2 | 4 |
v3 | Value 3 | 78 |
w3 | Weight 3 | 2 |
weighted_sum | Derived value= v1 * w1 + v2 * w2 + v3 * w3 | calculated |
weight_total | Derived value= w1 + w2 + w3 | calculated |
How It Works
How to Compute a Weighted Mean
Formula
Weighted Mean = (v1*w1 + v2*w2 + ... + vn*wn) / (w1 + w2 + ... + wn)
Each value is multiplied by its weight before summing. The result is then divided by the sum of all weights. This is useful when some observations matter more than others, such as course grades with different credit hours.
Worked Example
A student scores 85 (3 credits), 90 (4 credits), and 78 (2 credits). What is the weighted GPA?
v1 = 85w1 = 3v2 = 90w2 = 4v3 = 78w3 = 2
- 01Weighted sum = 85*3 + 90*4 + 78*2 = 255 + 360 + 156 = 771
- 02Total weight = 3 + 4 + 2 = 9
- 03Weighted mean = 771 / 9 = 85.6667
Ready to run the numbers?
Open Weighted Mean Calculator