The csapp says:
"Rounding toward even numbers avoids this statistical bias in most real-life situations. It will round upward about 50% of the time and round downward about 50% of the time."
And how to Prove it?
Round nearest down obviously has a bias rounding results down. Round nearest up obviously has a bias rounding results up. If you round nearest to even, then half the time you round up, half the time you round down. So the bias is gone. (Important for addition and subtraction, for multiplication the situation rarely arises, and for division or square root it doesn't happen at all).
Round nearest to even has other advantages. Take any x, y where x+y doesn't overflow. Let x' = (x + y) - y. x' isn't necessarily the same as x, due to rounding errors. But then let x'' = (x' + y) - y, and you will get x'' = x'. With round nearest down or up it can happen that if you repeat this, the result will slowly creep down or up.