What is my weighted average score?
Enter each value with its weight, one row per value, to get the weighted average.
- Weighted average
- 82.9
Weighted average of your values: 82.9.
- Sum of the weights
- 100
- Sum of value × weight
- 8,290
- Plain average
- 85
- Count
- 3
Weighted average: 82.9. Weighted average of your values: 82.9.
How to calculate
Computes the weighted average (weighted mean) of values from their weights, with the sum of the weights and the plain average for comparison.
Example with the default inputs (Values and weights [Value 92, Weight 20; Value 85, Weight 30; Value 78, Weight 50]): Weighted average of your values: 82.9.
Method: weighted average = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ)
- Each row holds one value and its weight.
- Weights cannot be negative, and at least one must be more than 0. They do not need to add up to 1 or 100.
- A weight of 0 leaves its value out of the weighted average.
Worked examples
Each example is checked against the calculator on every build.
- Values and weights 92 20; 85 30; 78 50 gives Weighted average 82.9, Sum of the weights 100, Sum of value × weight 8,290, Plain average 85.Source: hand calculation in content.mdx: (92 × 20 + 85 × 30 + 78 × 50) ÷ 100 = 8290 ÷ 100 = 82.9
- Values and weights 2 1; 3 1; 5 0; 7 0; 11 4; 13 1; 17 2; 19 1; 23 0 gives Weighted average 11.5, Sum of the weights 10, Sum of value × weight 115, Count 9.Source: NIST Dataplot Reference Manual, WEIGHTED MEAN (EQ 2-20) and its example data; hand calculation in content.mdx: 115 ÷ 10 = 11.5
- Values and weights 4 3; 3 4; 2 3 gives Weighted average 3, Sum of the weights 10, Sum of value × weight 30.Source: hand calculation in content.mdx: (4 × 3 + 3 × 4 + 2 × 3) ÷ 10 = 30 ÷ 10 = 3.0
How it works
For values x₁, x₂, …, xₙ with weights w₁, w₂, …, wₙ (the NIST Dataplot weighted mean, EQ 2-20):
weighted average = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ)
The calculator also shows:
- Sum of the weights: Σw = w₁ + w₂ + … + wₙ.
- Sum of value × weight: Σw·x = w₁x₁ + w₂x₂ + … + wₙxₙ.
- Plain average: (x₁ + x₂ + … + xₙ) ÷ n, each value counted once.
- Count: n, the number of values.
Assumptions
- Each row holds one value and its weight. Every row needs both, and there are 1 to 50 rows.
- Every weight must be 0 or more, and the weights must add up to more than 0; otherwise there is no answer.
- The weights do not need to add up to 1 or 100. Multiplying every weight by the same number does not change the weighted average.
Worked examples by hand
Course grade (the default). Homework 92 counts 20%, the midterm 85 counts 30%, and the final 78 counts 50%. The products are 92 × 20 = 1,840, 85 × 30 = 2,550, and 78 × 50 = 3,900, which add up to 8,290. The weights add up to 100. The weighted average is 8,290 ÷ 100 = 82.9. The plain average is (92 + 85 + 78) ÷ 3 = 85.
NIST's example data. Values 2, 3, 5, 7, 11, 13, 17, 19, 23 with weights 1, 1, 0, 0, 4, 1, 2, 1, 0. The weights add up to 10. The products are 2, 3, 0, 0, 44, 13, 34, 19, 0, which add up to 115. The weighted average is 115 ÷ 10 = 11.5.
GPA from credit hours. Grade points 4, 3, 2 for courses of 3, 4, and 3 credits. The products are 12, 12, and 6, adding up to 30, and the credits add up to 10. The GPA is 30 ÷ 10 = 3.0.
Other questions people ask
How do I calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. For scores of 92, 85, and 78 weighted 20%, 30%, and 50%, the products add up to 8,290, the weights add up to 100, and the weighted average is 8,290 ÷ 100 = 82.9.
Do the weights have to add up to 100% or to 1?
No. The calculator divides by the sum of the weights, so weights of 20, 30, and 50, of 0.2, 0.3, and 0.5, or of 2, 3, and 5 all give the same answer. Only the proportions between the weights matter.
What is the difference between a weighted average and a normal average?
A normal average counts every value once. A weighted average counts some values more than others. If every weight is the same, the two are equal. For the default example, the plain average is 85 but the weighted average is 82.9, because the final exam (78) carries half of the grade.
How do I work out my GPA with credit hours?
Enter the grade points of each course as the values (A = 4, B = 3, C = 2, D = 1, F = 0 on the usual US scale) and the credit hours as the weights. An A in a 3-credit course, a B in a 4-credit course, and a C in a 3-credit course give (12 + 12 + 6) ÷ 10 = 3.0.
What happens if a weight is 0?
A value with weight 0 has no effect on the weighted average. It still counts in the plain average shown for comparison. At least one weight must be more than 0, or there is nothing to divide by.
Can a weight be negative?
Not in this calculator. Weights stand for importance, shares, or counts, which cannot be below 0. With weights of 0 or more, the weighted average always lies between the smallest and the largest value.
How do I add more values?
Press Add row under the last row, then type the new value and its weight. Each row has a Remove button. You can enter up to 50 values.