Weighted Average Calculator (with Steps to Solve)

Enter the values in a data set and their respective weights to calculate the weighted average.

	Value	Weight
x₁		w₁
x₂		w₂
x₃		w₃
x₄		w₄
x₅		w₅
x₆		w₆
x₇		w₇
x₈		w₈
x₉		w₉
x₁₀		w₁₀
x₁₁		w₁₁
x₁₂		w₁₂
x₁₃		w₁₃
x₁₄		w₁₄
x₁₅		w₁₅
x₁₆		w₁₆
x₁₇		w₁₇
x₁₈		w₁₈
x₁₉		w₁₉
x₂₀		w₂₀
x₂₁		w₂₁
x₂₂		w₂₂
x₂₃		w₂₃
x₂₄		w₂₄
x₂₅		w₂₅

Weighted Average:

Steps to Find the Weighted Average

To find the weighted mean, use the following formula:

\bar{x} = \frac{\left (x_{1} \cdot w_{1} \right ) + \left (x_{2} \cdot w_{2} \right ) + ... + \left (x_{n} \cdot w_{n} \right )}{w_{1} + w_{2}+ ... + w_{n}}

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How to Find a Weighted Average

A weighted average, sometimes called a weighted mean, is an average value that reflects the varying amount of importance of each value in a data set. This is different from the arithmetic mean, where each value contributes equally when calculating the average.

Weighted averages are often used for applications such as sports statistics, class grades and GPA, job performance, credit scores, averaging the cost of capital (e.g. WACC), or calculating stock cost basis.

A classic example of weighted averages is the school course, where homework is worth a smaller portion of the grade than the final exam.

Weighted Average Formula

To calculate a weighted average or weighted mean, you can use the following formula:

\bar{x} = \frac{\sum_{i=1}^{n}x_{i} \cdot w_{i}}{\sum_{i=1}^{n}w_{i}}

This weighted average formula can be expressed more simply:

\bar{x} = \frac{\left (x_{1} \cdot w_{1} \right ) + \left (x_{2} \cdot w_{2} \right ) + … + \left (x_{n} \cdot w_{n} \right )}{w_{1} + w_{2}+ … + w_{n}}

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Thus, the weighted average x̄ is equal to the sum of the products of each weight and its value, divided by the sum of the weights.

Graphic showing the weighted average formula where the weighted average is equal to the sum of the products of each value and weight divided by the sum of the weights.

For example, let’s use the weighted average formula to calculate a student’s grade average with the following courses and grades:

class 1: 4 credits B (3.0)
class 2: 3 credits A (4.0)
class 3: 4 credits A- (3.7)
class 4: 3 credits B+ (3.3)

GPA = \frac{\left (3.0 \cdot 4 \right ) + \left (4.0 \cdot 3 \right ) + \left (3.7 \cdot 4 \right ) + \left (3.3 \cdot 3 \right )}{4+3+4+3}

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GPA = \frac{12.0+12.0+14.8+9.9}{4+3+4+3}

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GPA = \frac{48.7}{14}

GPA = 3.48

This student’s GPA is 3.48.

This example should demystify how weighted averages work. You might also be interested in learning more about the geometric mean.

Weighted Average Calculator