Media ponderata

Consider a data set where some values are more important than others; in other words, they carry more weight.

To calculate the mean for such data, each value is multiplied by its weight. The resulting products are added and then divided by the sum of weights.  This is called the weighted mean. 

For example, a student takes several tests in a year, each weighted differently. To determine the weighted mean of all the tests, multiply the individual test scores with the corresponding weights and add these products. Then, divide this final value by the sum of all the weights.  

As one can see, the students get better mean scores by doing well in tests with higher weights. That means, the data values with a higher weight contribute more to the weighted mean. 

If the weights of all the data values are the same, then the weighted mean is equal to the arithmetic mean.