But you mentioned average (mean). You can have the same average but different median, and only if you would talk about median it would be guaranteed that 50% of

But you mentioned average (mean). You can have the same average but different median, and only if you would talk about median it would be guaranteed that 50% of the cases are above and 50% under. In the case you mentioned, with an average, there might be extreme outliers that make the average different from the median, thus rendering the assertion that 50% of the cases are above the average and 50% under false.