Weighted mean

The weighted mean multiplies each value by a weight reflecting its relative importance, then divides by the total weight. It applies when observations do not contribute equally — for example, combining department averages of unequal size.

ByHoang TruongUpdated July 3, 2026

See it move

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Three warehouses report average unit costs of €40, €55 and €70. Treated equally, the simple average is €55.00. But the warehouses handled 500, 200 and 300 units respectively, so multiplying each cost by its volume — €20,000, €11,000, €21,000 — and dividing the €52,000 total by 1,000 units gives a weighted mean of €52.50, correctly reflecting the high volume at the cheapest site.

Where it fits

TopicDescriptive StatisticsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

\bar{x}_w = \frac{\displaystyle\sum_{i=1}^{n} w_i\, x_i}{\displaystyle\sum_{i=1}^{n} w_i}

Variables

$\overset{x}{ˉ}_{w}$: weighted mean (units of x)
$w_{i}$: weight assigned to observation i (dimensionless)
$x_{i}$: i-th observation (units of x)
$n$: number of observations (dimensionless)

Check yourself

PracticeCORE

Three product lines report average unit margins of €15, €25 and €40. The lines produced 4,000, 2,000 and 1,000 units respectively last quarter. A finance manager reports the company's overall average unit margin as €26.67, computed as (15 + 25 + 40) ÷ 3. What is the correct weighted-mean average unit margin?

Select an answer to check your understanding.