# What is my weighted average score?

Computes the weighted average (weighted mean) of values from their weights, with the sum of the weights and the plain average for comparison.

- Page: https://www.acalculator.org/statistics/weighted-average-calculator
- JSON spec: https://www.acalculator.org/statistics/weighted-average-calculator.json
- Version: bb309b7ce2cd

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| items | Values and weights | One row per value, with its weight. Weights may be percents, counts, or credits. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| weightedMean | Weighted average | The sum of each value times its weight, divided by the sum of the weights. |
| weightSum | Sum of the weights | All the weights added up, Σw. |
| productSum | Sum of value × weight | Each value times its weight, added up, Σw·x. |
| mean | Plain average | The ordinary mean of the values, with every value counted once, for comparison. |
| count | Count | How many values there are. |

## Method

weighted average = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ)

## Assumptions

- 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

1. items = {"value":92,"weight":20} or {"value":85,"weight":30} gives weightedMean = 82.9, weightSum = 100, productSum = 8,290, mean = 85. Source: hand calculation in content.mdx: (92 × 20 + 85 × 30 + 78 × 50) ÷ 100 = 8290 ÷ 100 = 82.9.
2. items = {"value":2,"weight":1} or {"value":3,"weight":1} gives weightedMean = 11.5, weightSum = 10, productSum = 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.
3. items = {"value":4,"weight":3} or {"value":3,"weight":4} gives weightedMean = 3, weightSum = 10, productSum = 30. Source: hand calculation in content.mdx: (4 × 3 + 3 × 4 + 2 × 3) ÷ 10 = 30 ÷ 10 = 3.0.

## FAQ

### 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.

## Sources

- NIST Dataplot Reference Manual, WEIGHTED MEAN (EQ 2-20), March 18, 1997. https://itl.nist.gov/div898/software/dataplot/refman2/ch2/weigmean.pdf
- NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.1, Measures of Location (the mean). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm