Weighted arithmetic mean | Statistics

A weighted arithmetic mean is a special use of the mean value. A weighted arithmetic mean can be used when the data is grouped into a frequency distribution or when there are many observations with the same value.

A weighted average is calculated by multipling each unique value by the number of times it has been observed (weight) and this sum is then divided by the sum of all the weights.

Weighted average: The sum of weight multiplied by value / sum of the weights

If we observe the value of five 10 times, the value of ten 5 times and the value of fifteen 10 times, then the weighted aritmetic mean is 10 (((5 * 10 + 10 * 5 + 15 * 10) / (10 + 5 + 10)). We would have got the same result if we had calculated the mean but it was easier to calculate the weighted average in this case.