**Instructions:** Use this Weighted Average Calculator to compute the weighted average of a set of values \(X\) and their associated weights. Please type in the values and the corresponding weights:

## What you need to know about this Weighted Average Calculator

The average, as a measure of central tendency is typically used in applications as a representative value, from a whole set of values \(X_1, X_2, ...., X_n\).

But sometimes, it turns out that not all values are equally important, and we would like to consider some values to be more important than others. This is achieved by using weights and the concept of weighted averages.

### When to use weighted average?

As it was mentioned above, the weighted average needs to be used when not all values in the sample are equally important, or said differently, not all the values in the sample carry the same weight.

Then, in that case, for each value \(X_i\) we associate a weight \(w_i\), which is a positive number, and it represents how important \(X_i\). The larger the \(w_i\) is, the more important \(X_i\) is in terms of its representativeness.

### Weighted average equation

The weighted average formula is based upon the values \(X_i\) and weights \(w_i\), and it corresponds to:

\[\text{Weighted Average}=\frac{\sum\limits_{i=1}^{n}{{{X}_{i}}{{w}_{i}}}}{\sum\limits_{i=1}^{n}{{{w}_{i}}}}\]This weighted mean calculator will show you how to use the above formula step-by-step.

### What if there are no weights?

Observe that if all the values in the data carry the same weight, this is, no value is more important than any other, then we should use this sample mean calculator, which does not go into the considering any weights to compute the average.

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