이 문제가 궁금했는데, 누군가 답변을 올려놓았다. 맞는 얘기인지는 ....

출처는 http://www.curiousmath.com/index.php?name=News&file=article&sid=30

Re: Round to Even
by mopslik
on Jul 13, 2004
While the term "proof" applied to this trick is horribly misleading -- it is a sample, or simulation -- it should also be pointed out that round-to-even is only more accurate in a cumulative sense. In other words, the accuracy of the rounding becomes an issue only when multiple operations are being carried out. This may not seem like a big difference, but it's important.

For example, in terms of individual numbers ending in 5 after the decimal place, round-up will always give an error of 0.5 (ie. 4.5 -> 5). Round-to-even will still give an error of 0.5 (ie. 5.5 -> 5) but there is a zero-sum associated with cumulative operations on data sets. In other words, when performing multiple operations with data, round-to-even will "cancel out" rounding errors to a greater extent than round-up.

Consider the data set {4.5, 5.5, 6.5, 7.5, 8.5}. Round-up yields {5, 6, 7, 8, 9}, whereas round-to-even yields {4, 6, 6, 8, 8}. Summing each of these sets, round-up yields 35, whereas round-to-even yields 32. The actual sum of the original data set is 32.5, which supports the claim that round-to-even is more accurate. Examining the rounding adjustments made during calculations, round-up yields {+0.5, +0.5, +0.5, +0.5, +0.5}, whereas round-to-even yields {-0.5, +0.5, -0.5, +0.5, -0.5}. The sums of these data sets are 2.5 and -0.5 respectively, where a number closer to zero is more accurate.

The original post hints at this when it describes the Rounding Error, but does not make it explicitly clear why this is the case. Hopefully this post will clarify.