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MasterMath

Weighted Average Calculator

A weighted average where some values count more than others, shown next to the plain average so the difference is visible.

Weighted average

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Weighted average—
Plain average—
Difference between them—
Sum of the weights—
How many values—

Each value and its weight

ValueWeightProduct

How this was worked out

    The rule

    weighted average = Σ(value × weight) ÷ Σ(weights)

    Why it works

    A weighted average lets each value contribute in proportion to its weight rather than equally. Multiply each value by its weight, add those products, and divide by the total weight.

    How to do it by hand

    1. Multiply each value by its weight
    2. Add all those products
    3. Add all the weights
    4. Divide the first total by the second

    What is worth knowing

    The plain average is the special case where every weight is the same, which is why the two agree when the weights are equal. Weighted averages turn up wherever contributions differ in importance: course grades where the exam counts more than the coursework, portfolio returns weighted by how much is invested in each holding, and price indices weighted by how much of each good people actually buy. The weights need not add to 100 — only their proportions matter, which is why 30/50/20 and 3/5/2 give the same answer.

    Frequently asked questions

    When is a weighted average the right one?

    Whenever the values do not deserve equal say: grades with different weightings, returns on different investment sizes, price indices.

    Do the weights have to add to 100?

    No. Only their relative sizes matter, so 30/50/20 and 3/5/2 give the same result.

    Why does it differ from the plain average?

    Because the plain average weights everything equally. They agree only when the weights are all the same.

    Can a weight be zero?

    Yes, and it simply excludes that value. Negative weights are a different matter and rarely mean anything sensible.