halfeven is a rounding rule to preserve statistical properties

quoted from wikipedia under the fair use assumption

Round half to even

A tie-breaking rule that is even less biased is round half to even, namely

If the fraction of y is 0.5, then q is the even integer nearest to y.

Thus, for example, +23.5 becomes +24, +22.5 becomes +22, âˆ’22.5 becomes âˆ’22, and âˆ’23.5 becomes âˆ’24.

This method also treats positive and negative values symmetrically, and therefore is free of overall bias if the original numbers are positive or negative with equal probability. In addition, for most reasonable distributions of y values, the expected (average) value of the rounded numbers is essentially the same as that of the original numbers, even if the latter are all positive (or all negative). However, this rule will still introduce a positive bias for even numbers (including zero), and a negative bias for the odd ones.

This variant of the round-to-nearest method is also called unbiased rounding (ambiguously, and a bit abusively), convergent rounding, statistician's rounding, Dutch rounding, Gaussian rounding, or bankers' rounding. This is widely used in bookkeeping.

This is the default rounding mode used in IEEE 754 computing functions and operators.

the average of two numbers will be preserved

truncation

22.5 ==> 22

23.5 ==> 23

the averages

23 vs. 22.5

half to even

22.5 ==> 22

23.5 ==> 24

the averages

23 vs. 23