No idea why you think median income has any relevance here. You could of course define "middle class" like that, but that is not the actual meaning of the term. I think in Western societies your middle class is at best 10% of people nowadays.
And just to add: I think this widespread redefinition of what middle class is not an accident. It seems quite effective, if you think 50k USD is middle class in the US. It wouldn't even be middle class in most of poorer Europe. The idea of term is completely unrelated to relative income, but rather a different social status; that isn't the case if you live paycheck to paycheck. And this redefinition is happening to obscure the fact that a large part of our population in the West had a loss in living standards over the last decades.