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Weighted Average Calculator

By Calxy · Updated · Calculation methodology

Find an average where some values count more than others. Enter the values and their weights; the weights do not need to add up to 100.

Printed from Calxy · https://www.calxy.net/math/weighted-average-calculator

Weighted average82.0000

The numbers to average, such as test scores, separated by commas.

How much each value counts, in the same order. Weights cannot be negative.

Weighted average

82.0000

  • Total weight100.0000
  • Number of values3

Weights can be counts, percentages or relative importance; they do not need to sum to 100. Zero weights contribute nothing.

How this was calculated

  1. Multiply every value by its corresponding weight (how much it counts).value × weightPut in your numbers: 80 × 20 = 1600; 90 × 50 = 4500; 70 × 30 = 2100
  2. Add up all of those answers.Σ(value × weight)Put in your numbers: 1600 + 4500 + 2100Answer: 8200
  3. Add up the weights to get the total weight.Σ weightPut in your numbers: 20 + 50 + 30Answer: 100
  4. Divide the sum of those products by total weight. That is the weighted average.Weighted average = Σ(value × weight) ÷ Σ weightPut in your numbers: 8200 ÷ 100Answer: 82

Weighted averages in simple words

A weighted average is an average where some numbers count more than others. The weight says how much each number counts.

Multiply each number by its weight, add those answers up, then divide by the total of the weights.

For example, say tests are worth 20%, the project 50% and homework 30%, and you scored 80, 90 and 70. Then 80 × 20 + 90 × 50 + 70 × 30 = 1,600 + 4,500 + 2,100 = 8,200. The weights add up to 100, so the weighted average is 8,200 ÷ 100 = 82.

A normal average of 80, 90 and 70 would be 80. The weighted average is higher because the 90 counts the most.

Formula and method

Weighted mean = Σ(value × weight)/Σweight. At least one weight must be positive.

Worked example

Values 80, 90 and 70 weighted by 20, 50 and 30 give (1600 + 4500 + 2100)/100 = 82.

Frequently asked questions

Can a weight be zero?

Yes. A zero-weight value contributes nothing. Negative weights are excluded from this ordinary weighted-average tool.

Last updated . Results are estimates for informational purposes only.