>So, rounding 5.5 to 6 would be the correct and appropriate thing to do ( i.e. normal rounding ). But are you saying that some one could legitimately, in determining a median, "round" $5.01 to 6 and call that "correct"?

Yes, if you're the phone company computing a bill, 1 second becomes 1 minute, that's the kind of thing I was semi-joking about :)

But not normally, in truly objective work. However, you can find a basis for rounding 5.5 to 5, that is done in some systems/methodologies.