What Does ½ Really Round Off To?

[yearofglad]

A previous thread on rounding:

Traditional rounding 'bias'. I don't get it.

In elementary school when I was taught how to round numbers to a whole number, I was taught that if the last digit ends in 0, 1, 2, 3, or 4, round down to ‘0’. Otherwise round up to the next digit. But later on, I was told that this introduces bias and that there are different techniques to deal with it. So I want to believe that it does cause bias because people much smarter than me in this have developed these techniques to reduce it. But I can’t convince myself of it. Can someone explain t…