With some minor assumptions, my assertion would be correct. Yours needs a lot of strong assumptions to be mathematically feasible. Basically, you are saying, w

With some minor assumptions, my assertion would be correct. Yours needs a lot of strong assumptions to be mathematically feasible. Basically, you are saying, when the max of a sequence is increasing, the mean/median stays or even decreases. That would require that the frequencies on the lower end to increase much faster than that on the higher end, which is certainly not the case. For example, the number of C programmers is growing faster than the number of Java programmer today? No one would think that's correct.