Brass Tilde wrote:
The problem with the grade-school rule is that, assuming the
last digit is uniformly distributed, you'll be rounding up 5
times out of 9 and rounding down 4 times out of 9.
No, if the last digit is uniformly distributed, then 0 is as likely as any
other. You round down on 0, 1, 2, 3 & 4 and round up on 5, 6, 7, 8 & 9.
The fact that rounding down on 0 is the same as the unrounded number isn't
significant.
A quote on rounding rules to limit bias -
There are three general rules for rounding:
* Rule 1- if the remainder beyond the last digit to be reported is
less than 5, drop the last digit. Rounding to one decimal place, the
number 5.3467 becomes 5.3.
* Rule 2-if the remainder is greater than 5, increase the final
digit by 1. The number 5.798 becomes 5.8 if rounding to 1 digit.
* Rule 3- To prevent rounding bias, if the remainder is exactly 5,
then round the last digit to the closest even number.Thus the number
3.55 (rounded to 1 digit) would be 3.6 (rounding up) and the number
6.450 would round to 6.4 (rounding down)if rounding to 1 decimal.
See page 12 in Hurlburt, R. (1994) Comprehending Behavioral
Statistics, Brooks/Cole, Pacific Grove, CA.
