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The "round to even" does NOT produce a bias
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".
The "round to even" does NOT produce a bias
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. |
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