Weighted average calculator

How do I calculate a weighted average?

Multiply each value by its weight, add the results and divide by the total weight. Scores of 90 worth 40% and 80 worth 60% average to (90 × 40 + 80 × 60) ÷ 100 = 84.

How do I enter the numbers?

One pair per line: the value, then its weight — "90 40" or "90, 40%". Weights can be percents, credits, units or any counts.

Do the weights have to add up to 100?

No — the calculator divides by whatever they add up to, so 2 and 3 work as well as 40% and 60%.

How is it different from a regular average?

A regular average counts every value the same. In the example it would be 85; the weighted average is 84 because the 80 counts more.

Where are weighted averages used?

Course grades, GPA with credit hours, the average price of shares bought at different prices, and survey results.

How do I find the mean of a frequency table?

Use the frequencies as the weights. If the table gives intervals, take each interval’s midpoint as its value, multiply by the frequency, add up and divide by the total frequency (OpenStax Introductory Statistics 2e, section 2.5). The worked example below does this for a class of 19.

What score do I need on the final to reach a target grade?

Solve the weighted average for the missing score: (target × 100 − grade so far × weight done) ÷ weight of the final. With 60% of the course done at 84, a final worth 40% and a target of 90, that is (90 × 100 − 84 × 60) ÷ 40 = 99. Enter 84 with weight 60 and 99 with weight 40 to check: the result is 90.

How the formula works

With values x₁ … xₙ and weights w₁ … wₙ, the weighted average is Σ(wᵢ × xᵢ) ÷ Σwᵢ. Wolfram MathWorld defines the weighted mean with nonnegative weights that add up to 1, so no division is needed; dividing by the total weight, as the calculator does, scales any set of weights to that form. That is why percents, credit hours and counts all work. Equal weights give the ordinary average. Weights must not be negative or all zero.

Worked example: a grouped test-score table

OpenStax Introductory Statistics 2e, section 2.5, estimates the mean of a class of 19 from score intervals. Each interval’s midpoint stands in for its scores and is weighted by its frequency: 53.25 × 1 + 59.5 × 0 + 65.5 × 4 + 71.5 × 4 + 77.5 × 2 + 83.5 × 3 + 89.5 × 4 + 95.5 × 1 = 1460.25. Divided by the 19 students, the estimated mean is 76.86, as in the book. An interval with frequency 0 changes neither total.

Common mistakes

Averaging averages: class A averaged 80 with 10 students and class B averaged 90 with 30, so the plain average of 80 and 90 is 85, but the combined mean is 87.5 because class B is three times as large. Dividing by 100 when only part of the course is graded: a 90 in a category worth 40% is an average of 90 so far, not 36. Swapping the two numbers on a line: the calculator expects the value first, then the weight.

Sources: Wolfram MathWorld, “Weighted Mean” (definition); OpenStax, Introductory Statistics 2e, section 2.5 “Measures of the Center of the Data” (mean of a frequency table, test-score example). Related tools: average calculator, GPA calculator, grade calculator and stock average calculator. How we check our calculators.