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.
Er, uh, I think it is. The average amount added is greater than the
average amount subtracted.
Suppose you start with twenty numbers:
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3,
1.4, 1.5, 1.6, 1.7, 1.8, 1.9 which sum to 19. (Pair 0.1 and 1.9, 0.2 and
1.8, etc., and you have 9 sums of 2 plus the 0.0 and 1.0 left over)
If you use the rule "x.5 rounds to x+1" rule the sum of the rounds is 20
because round(0.5)+round(1.5) = 3.
The rule "round x.5 to the nearest even" fixes this.
Gerry
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Gerry Snyder
American Iris Society Director, Symposium Chair
in warm, winterless Los Angeles -- USDA zone 9b, Sunset 18-19
