Weighted Mean Calculator

What the weighted mean calculator does

An ordinary average treats every value as equally important. A weighted mean does not. It lets some values count for more than others, which is how a final exam can matter more than a quiz, or a large holding can matter more than a small one. This calculator works out that weighted average from your values and the weight you give each one.

You enter each value with its weight, adding as many rows as you need, and it returns the single figure that balances them all. Below is how it does that, and how to think about the weights.

How to use it

1. Enter a value and its weight on each row. The value is the number itself, and the weight is how much it should count.
2. Add or remove rows with the buttons, so you have one row for every value in your set.
3. Press Calculate for the weighted average, or Reset to clear it.

How the weighted mean is worked out

Each value is multiplied by its weight, those products are added up, and the total is divided by the sum of the weights:

Weighted mean = (value × weight, summed for every value) ÷ (sum of the weights)

Dividing by the total weight at the end is the step that makes it work no matter what your weights add up to. If every weight were the same, the weights would cancel out and you would be left with the ordinary average, which is a neat way to see that the plain mean is just a weighted mean where everything counts equally.

What the weights really mean

The weights say how much each value matters, relative to the others. Only that relative size counts, not the actual numbers you use. Weights of 1, 2, and 3 give exactly the same result as 10, 20, and 30, because the second value is twice the first and the third is three times it in both cases.

That is why weights turn up in so many disguises. In a course grade they are percentages that add up to 100. In a grade point average they are course credits. In a share portfolio they are the number of shares held. You can use whatever units are natural to your problem, as long as every weight is zero or positive and they are not all zero.

A worked example: a course grade

Say a course grade is built from homework worth 20 percent, a midterm worth 30 percent, and a final worth 50 percent, and you scored 85, 78, and 92.

Multiply each score by its weight and add them: (85 × 20) + (78 × 30) + (92 × 50) = 1700 + 2340 + 4600 = 8640. Then divide by the total weight, 20 + 30 + 50 = 100, giving 86.4. The plain average of 85, 78, and 92 is 85, so the final exam, carrying half the grade, pulled the result up to 86.4. That shift is the weighting doing its job.

Entering your values and weights

Every row needs both a value and a weight for the calculator to run, so fill in each pair before calculating. Add a row for each new value with the Add Inputs button, and remove the last one with Remove Inputs, down to a minimum of two rows.

The weighted average is shown to four decimal places with trailing zeros trimmed. One thing worth remembering: a weighted mean can still be pulled by an outlier that carries a large weight, so a single heavily weighted value has a lot of say in the result.

Questions people ask

What is a weighted mean?

An average where each value carries a weight that sets how much it counts. Values with larger weights pull the result toward themselves more than values with smaller weights.

How is it different from a normal average?

A normal average gives every value equal say. A weighted mean lets you make some values count for more. If all the weights are equal, the two give the same answer.

Do the weights have to add up to 100?

No. Only the relative sizes of the weights matter, so 1, 2, 3 works the same as 10, 20, 30. Dividing by the total weight at the end handles any set of weights.

Where is the weighted mean used?

Course grades and GPAs, where categories or credits set the weights, and finance, where the size of each holding sets the weight. Anywhere some values genuinely matter more than others.

References

A quick note on where the methods here come from. The weighted mean and the way it generalises the ordinary average are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers the weighted mean and its common uses.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of location). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (measures of the center of the data). https://openstax.org/details/books/introductory-statistics-2e