How to Calculate a Weighted Average (With Examples)

A plain average gives every value the same say. A weighted average lets some values count more than others, which is what you need whenever the items in your list are not equally important or not equally large. Weighted averages underpin weighted GPAs, final exam scores, portfolio returns, and blended household budgets.

What Weighted Average Means

A weighted average is the sum of each value multiplied by its weight, divided by the sum of the weights. The weights express how much each value matters relative to the others. Weights do not have to be percentages or add up to 100, only the ratio between them matters.

The Formula

Weighted average = (Sum of each value times its weight) divided by (Sum of all weights). If you are given weights as percentages that total 100, you can skip dividing by the total, but dividing anyway is safer and lets you enter weights that do not total exactly 100.

Worked Example With Exam Scores

Three test scores of 60, 70 and 90 carry weights of 1, 1 and 2 because the final exam counts double. Multiply: 60 times 1 is 60, 70 times 1 is 70, 90 times 2 is 180. Add the products: 60 plus 70 plus 180 is 310. Add the weights: 1 plus 1 plus 2 is 4. Divide: 310 divided by 4 is 77.5. A plain average would have given 73.33, understating the result because it ignored that the highest score counted twice.

Worked Example With a Household Budget

Suppose 60 percent of spending goes to fixed costs at 1,200 per month and 40 percent to variable costs at 900 per month. Multiply: 1,200 times 0.6 is 720, and 900 times 0.4 is 360. Add: 1,080. Divide by the total weight of 1.0, giving 1,080. This is the figure that reflects the mix you actually have rather than an unweighted midpoint of two numbers you may never spend evenly across.

Choosing Sensible Weights

Weights should reflect genuine importance, not convenience. Using 1, 2, 3 because those are the ranks you assigned is fine only if the rank really is the importance. If the weights come from actual magnitudes such as hours, units, dollars or headcounts, the result will be far more defensible.

When All Weights Are Equal You Get a Plain Average

If every weight is the same, the weights cancel and you are left with the ordinary arithmetic mean. This is a useful sanity check: entering 1, 1, 1 as the weights should reproduce the mean, and the calculator is tested against exactly this case.

Mistakes That Produce the Wrong Answer

The two common errors are dividing by the number of values instead of the sum of the weights, and entering weights that do not line up with the values. Dividing by the count is only correct when all weights are equal. A mismatch between the number of values and the number of weights is rejected by the calculator rather than silently ignored.

Zero and Negative Weights

Weights that all sum to zero produce a division by zero and no meaningful answer, so the calculator blocks it. Negative weights are occasionally meaningful in advanced statistics for extrapolation, but for everyday averages and grades they are almost always a typo and should not be used.

How to Calculate a Weighted Average