The average is actually a statistical measure. It is sometimes used as a estimation measure (guess) for the true average of a larger population.

Yes the average is not perfect but it does capture some/partial information from a sample. The median does a better job dealing with outliers/extreme values. 50% of values are above the median and 50% of values are below the median.

Many people understand averages better than medians, variance, standard deviations, etc. so that is why it is used often.