Weighted Average Calculator

How to calculate Weighted Average manually?

You can calculate a weighted average by hand with a simple formula. The formula gives each value importance based on its weight.

Formula

$Weighted\ Average = \frac{(Value_1\times Weight_1)+(Value_2\times Weight_2)+...}{Weight_1+Weight_2+...}$

Step by step Guide

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

Practical Example

For $80$ with weight $2$ and $90$ with weight $3$, use $((80\times2)+(90\times3))\div(2+3)=86$. The weighted average is $86$. The score of $90$ matters more because it has the larger weight.

Weighted vs. Unweighted GPA

A weighted average combines scores with weights. GPA often uses course credits as weights, while weighted GPA may add points for harder classes. Your school sets GPA rules, so check its grading scale.

Formula

$College\ GPA=\frac{\sum(Grade\ Points\times Credits)}{\sum Credits}$

Step by step Guide

1. Convert each course grade to grade points.
2. Multiply grade points by credits.
3. Add the products.
4. Divide by total credits.

Example

$3.0$ points for $3$ credits and $4.0$ points for $2$ credits gives $((3\times3)+(4\times2))\div5=3.4$.

Arithmetic vs. Geometric vs. Harmonic Average

These averages answer different questions. The arithmetic average works well for ordinary scores. The geometric average works with growth rates, while the harmonic average often works with rates.

Formula

Arithmetic: $A=(x_1+x_2+...+x_n)\div n$

Geometric: $G=\sqrt[n]{x_1x_2...x_n}$

Harmonic: $H=n\div(1/x_1+1/x_2+...+1/x_n)$

Step by step Guide

1. Use arithmetic average for ordinary scores.
2. Use geometric average for rates or growth.
3. Use harmonic average for rates such as speed.
4. Use weighted average when values have different importance.

Practical Example

For $10$ and $20$, the arithmetic average is $15$. If weights are $1$ and $3$, the weighted average is $17.5$.