# Weighted Average Calculator

**A Weighted Average**, as the name suggests, is an average in which numbers have different weights relative to each other.
The most common example of its use is the counting of the weighted average of grades.
Calculating this average is slightly more complicated than counting the arithmetic mean,
but our weighted average calculator below will make this task much easier.

## Weighted average: formula and definition

The weighted average of *n* numbers *a1*, *a2*, ..., *an* with weights *w1*, *w2*, ..., *wn* (which are non-negative) is:

How to calculate the weighted average? Summarize all the numbers multiplied by their weights and divide the result by the sum of all the weights.

### Use of weighted average

The weighted average of school grades is probably the most common place where the weighted average is used. Apart from the case of use shown above, where the teacher uses it to grade students, it is possible to imagine that such a weighted average could be used for enrolment. For example, for computer science studies, the grades in mathematics and physics would have a higher weighting and the grades in biology or physical education would have a much lower weighting.

Product rating - when evaluating products, we can determine which product features are most important to us and give them appropriate weighting.
For example, for a mobile phone we can determine the following features and weights:
photo quality 40%, i.e. weight 4, battery size 30%, i.e. weight 3, memory amount 20%, weight 2, processor speed 10%, weight 1.
Now let's assume that we have two phones:

- *phone 1*, which we will evaluate - photo quality 8 (out of 10), battery size 5, memory 6, processor speed 8

- *phone 2* receives ratings - photo quality 9 (out of 10), battery size 5, memory 3, processor speed 7

For *phone 1* the weighted average is *6.70* and for *phone 2* it is *6.40*

Calculation of stock market indices - one of the best-known stock market indices in the world is *S&P 500*.
It consists of the 500 largest American public companies and its index is the weighted average of their capitalization