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Weighted Average Calculator
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Other tools you may find usefulWeighted average - definition, concept of weights and statistical significance
Weighted average is a statistical concept that is an extension of the classic arithmetic mean. While in the arithmetic mean each element of the set has exactly the same meaning, in the weighted average individual numbers are assigned the so-called weights (importance markers). Elements with a higher weight have a greater impact on the final average result than those with a lower weight. Weighted average is a basic tool in school and academic assessment, as well as in finance (for calculating the profitability of investment portfolios), economics (calculating inflation rates) and in logistics.
Our intuitive online weighted average calculator allows you to instantly add additional ratings or financial values, assign them weights and immediately calculate the final average with an accuracy of several decimal places.
Formula for calculating the weighted average
To calculate the weighted average for the set of valuesx₁, x₂, ..., xnwith their respective weightsw₁, w₂, ..., wn, the following formula is used mathematical:
Weighted average = (x₁ × w₁ + x₂ × w₂ + ... + xn× wn) / (w₁ + w₂ + ... + wn)
In other words: we multiply each value by its weight, sum all the resulting products, and then divide this sum by the sum of all weights. If all weights were equal (e.g. equal to 1), the weighted average would reduce exactly to the classic arithmetic average.
Table with an example: calculating the student's average semester grade
The table below shows the grades collected by the student during the semester with the weights assigned to them:
| Type student's activity | Grade obtained (x) | Grade weight (w) | Product of grade and weight (x × w) | Comparison with the arithmetic mean |
|---|---|---|---|---|
| Test (class) | 5 | 5 | 25 |
Arithmetic mean: (5 + 4 + 2 + 5) / 4 =4.00 Weighted average: 51 / 12 =4.25 |
| Test (class) | 4 | 5 | 20 | |
| Oral answer | 2 | 1 | 2 | |
| Homework | 5 | 1 | 5 | |
| SUM: | - | 12 (Sum of weights) | 51 (Sum of products) | The weighted average is higher because the student received better grades on the highest priority assignments |
Use of weighted average in finance and economy
Outside the grading system in schools, weighted average is commonly used in schools. business:
- WACC (Weighted average cost of capital):A key financial indicator of enterprises, determining the cost of obtaining capital from various sources (debt, shares), where the weights are the shares of individual sources in the capital structure.
- Inflation (CPI):The Central Statistical Office (GUS) calculates the inflation rate as the weighted average of the price increase of individual goods and services. The weights are the share of these goods in the average shopping basket of a Polish family (e.g. the increase in food prices weighs more than the increase in theater ticket prices).
Frequently asked questions (FAQ)
How to calculate weighted average?
Multiply each number in the set by the weight assigned to it, sum these results, and then divide them by the sum of all weights.
What is the difference between weighted average and arithmetic average?
In the arithmetic mean, each number has the same meaning. In a weighted average, some values are more important than others, as determined by the weights assigned to them.
How to calculate grade point average if grades have weights?
We use the weighted average formula. For example, a rating of 5 with a weight of 4 and a rating of 3 with a weight of 2 gives: (5 × 4 + 3 × 2) / (4 + 2) = (20 + 6) / 6 = 26 / 6 = 4.33.
Can the weights in a weighted average be fractional?
Yes, the weights do not have to be integers. They can be decimals, fractions or percentages (as long as their sum in the denominator is not zero).
What to do if the weight of an item is zero?
An element with a weight of zero does not affect the final result of the weighted average - its product in the numerator will be zero, and the weight will not increase the sum of the weights in the denominator.