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The "round to even" does NOT produce a bias
Authored by: mikemccallum on Dec 12, '05 02:45:33PM

0 is a digit, as is 1,2,3,4,5,6,7,8,9. Count them. Yup, there is 10 of them. Rounding up on 5,6,7,8,9 gives 5 chances to round up. Truncating on 0,1,2,3,4 gives 5 chances to truncate. It is a lazy analysis which states that "rounding up on 5 introduces a bias".

Zero can be a certain, significant, or uncertain digit just as any of the other nine.

This is, of course, totally to the side of the issue with the calculator function.

The "round to even" does NOT produce a bias
Authored by: peterneillewis on Dec 12, '05 07:29:24PM

To say this is a lazy analysis while providing such a flawed analysis is impressive. If you sum the changes from 0-4 rounding down and 5-9 rounding up, you get 0 + 1 + 2 + 3 + 4 for rounding down (total 10) and 5 + 4 + 3 + 2 + 1 for rounding up (total 15). On the other hand, if you round to even, then the total changes for rounding down is 0 + 1 + 2 + 3 + 4 + (half of 5), and for rounding up is (half of 5) + 4 + 3 + 2 + 1, which you will note is 12.5 for both.

Rounding to even does generate a bias in the distribution towards even numbers, but for most purposes a slight bias towards even numbers is better than a slight bias upwards.