It's almost certainly true, perhaps doing a weighted average of the medians of subgroups. However, any method that does that is not producing a median. A good way of doing that adjustment might give "cooked" numbers for the various options, but the point where 50% are below and 50% are above would still almost certainly be an integer. And if it is actually balanced (highly unlikely with so many data points), so that any number greater than X and less than X+1 divides the population in two, then the convention is to report X + 1/2. There is no information about the median that anything past the decimal point can actually convey.