Weighted Mean Calculator
Find the weighted average of values with weights.
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How it works
A weighted mean is an average in which some values count more than others, and this calculator computes it from a list of values and a matching list of weights. You enter both lists, and it multiplies each value by its weight, adds up the results, and divides by the total of the weights. Unlike a simple average, where every value contributes equally, a weighted mean lets you reflect that some data points are more important, more frequent, or more reliable than others. The most familiar example is a course grade where exams count more than quizzes: an exam weighted at 50 percent influences the final mark far more than a homework worth 10 percent. Weighted means appear everywhere: in grade point averages weighted by credit hours, in stock indices weighted by market capitalisation, in survey results weighted to match a population, and in cost averages weighted by quantity. Students, teachers, analysts, and researchers all rely on them. The weights can be percentages, counts, or any positive numbers, since only their relative sizes matter. When every weight is the same, the weighted mean equals the plain arithmetic mean. Enter the values and their weights, in the same order, to compute the weighted mean.
weighted mean = Σ(value × weight) / Σweight
The weighted mean multiplies each value by its weight, sums those products, and divides by the sum of the weights. Weights represent the relative importance of each value, so values with larger weights pull the average toward them more strongly. When all weights are equal, the weighted mean reduces to the ordinary arithmetic mean, making it a general form of averaging.
Source:Descriptive statistics
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Worked example
How to use this calculator
- 1
Enter your values
Enter values and weights.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Weighted mean updates instantly as you type — no button to press.
Frequently asked questions
What is a weighted mean?
A weighted mean is an average that gives different importance, or weight, to each value rather than treating them all equally. Each value is multiplied by its weight, the products are summed, and the total is divided by the sum of the weights. Values with larger weights influence the result more, which is useful when some data matter more than others.
How is it different from a simple average?
A simple, or arithmetic, average treats every value equally, adding them and dividing by the count. A weighted mean assigns each value a weight reflecting its importance or frequency, so values can count more or less. When all weights are equal, the two are identical; the weighted mean is the more general form that reduces to a simple average as a special case.
How do I calculate a weighted grade?
Multiply each score by its weight, such as an exam worth 50 percent or homework worth 20 percent, sum those products, and divide by the total weight. Enter your scores and their weights into the calculator to get the weighted grade. This reflects how much each component contributes to your final mark, which a simple average would ignore.
Do the weights need to add up to 100?
No. Only the relative sizes of the weights matter, because the formula divides by the sum of the weights. You can use percentages that total 100, raw counts, credit hours, or any positive numbers, and the result is the same as long as the proportions are preserved. The calculator handles any weight totals correctly.
Where are weighted means used?
Weighted means appear in grade point averages weighted by credit hours, stock market indices weighted by company size, economic indicators weighted by population or spending, survey data adjusted to represent a population, and average prices weighted by quantity purchased. Any time some values should count more than others, a weighted mean gives the correct average.