Weighted Mean & Median

If we are given the distribution only & not given the weights for the mean, how weighted mean is calculated.


Hello @sharathnandalike,
This is an interesting question.

In the calculation of the mean, the elements of the distribution are assumed to have the same weight (=1). Here are some cases that can guide the choice: (weighted mean vs. mean)

  • If we have a distribution and all the values are present (i.e., also repeated values are present, no aggregation), we can calculate the mean, which is a weighted mean where the weights are equal to 1.

  • If we have a distribution with only distinct values, and we are sure that repetitions are not possible, the mean is also enough.

  • If we have an aggregated distribution, i.e., only the distinct values are present, and each of them has an aggregated value ** associated with it, we have to use weighted mean because the additional information has to be used in any way.

**An aggregated value can be the number of times that a value is present, the probability of that value, or any other value that provides information about the quantity of a value in the distribution.

Thank you for this interesting question. Don’t hesitate if you have any other questions.