This cracks me up because it is often said with such confidence, but it is just wrong.
If you have 10 people, 8 have an intelligence score of 1, 1 has a score of 5 and 1 has a score of 10. The average is 2.3 which means that 80% of the people are below average.
The median is the only thing that is going to guarantee 50%.
Depending on the context, the most representative statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, or mode.