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Weighted Mean

Also called: weighted average

Definition: A weighted mean is an average in which each value is multiplied by a weight reflecting its importance or frequency, then divided by the sum of the weights.

Updated November 9, 2026 · How we check facts

A weighted mean assigns each value a weight and gives heavier-weighted values more influence on the result. OpenStax describes it as the sum of the value-times-weight results divided by the sum of the weights. Grades with different percentages, shares bought at different prices and combined group averages all use it. A frequency table is a special case where each weight is the number of times the value occurs.

Formula

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

value: each number being averaged.
weight: its importance or count.

Example

Homework 90 (40%), midterm 80 (35%), project 70 (25%): 90 × 0.40 + 80 × 0.35 + 70 × 0.25 = 36 + 28 + 17.5 = 81.5, and the weights add to 1, so the weighted mean is 81.5. The plain arithmetic mean would be 80.

Combining a class of 20 students averaging 80 with a class of 5 averaging 60: (20 × 80 + 5 × 60) ÷ 25 = 76, not 70.

See the guide to calculating an average, the final grade guide and weighted GPA for related uses.

Calculate it

Free toolAverage CalculatorMean, median, mode and more from any list of numbers.Open →Free toolGrade CalculatorYour class grade from scores and weights.Open →

Guides that explain it

Related terms

Arithmetic MeanThe arithmetic mean is the sum of a set of values divided by how many values there are; it is the number most people mean by "the average".Weighted GPAA weighted GPA is a grade point average that awards extra points for harder courses such as honors, AP or IB, so an A in an advanced class can count for more than 4.0.Absolute ZeroAbsolute zero is 0 K, the lowest point of the kelvin temperature scale. On the Celsius scale it equals −273.15 °C, and on the Fahrenheit scale about −459.67 °F.Celsius (°C)Celsius is a temperature scale in which one degree has the same size as one kelvin, with 0 °C equal to 273.15 K; water freezes near 0 °C and boils near 100 °C at standard pressure.Fahrenheit (°F)Fahrenheit is the temperature scale used for everyday weather and cooking in the United States; a degree is 5/9 the size of a Celsius degree, and 32 °F equals 0 °C.Greatest Common Factor (GCF)The greatest common factor (GCF) of two or more positive integers is the largest whole number that divides each of them with no remainder; it is also called the GCD or HCF.International System of Units (SI)The International System of Units (SI) is the modern metric system: seven base units, including the meter, kilogram, second and kelvin, with prefixes that scale by powers of ten.Kelvin (K)The kelvin is the SI base unit of temperature. It starts at absolute zero (0 K), and one kelvin is the same size as one degree Celsius, with 0 °C equal to 273.15 K.

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