We're assuming in this totally contrived example that points are a measure of total resources + opportunity in our closed system, since we're implying a redistribution of a fixed pool of resources^1.

So, the total in the "after" picture would still be 94 and thus the mean would remain at 9.4 and the median would be 9.4 - (and down from 10).

I'm not a fan of arguing from averages - realistically, the picture is more like 1 - 1000pts, 2 - 100pts, 3-50pts, 4-30pts, 5, 6-7 - 20pts, 8-10 10pts

~ 1270 total, avg 127, median 20.

But these are all contrived examples (in the above I'm more leaning on income distribution, which I've reproduced from memory and may be skewed). If we equalize the above, the median would go up.

The argument for redistribution can be made on an economic/statistical basis - but the argument for equality, I think, is ultimately moral. It's not about fairness per se, but about justice.

^1 Not quite my stance but for the sake of argument.