From: Wybo Dekker <wybo@...4all.nl>
Date: 2012-07-17T05:36:06+09:00
Subject: Re: rounding to nearest even: nio gem?

On 2012-07-16 17:15, Bartosz Dziewoński wrote:
> I'm not sure I understand what exactly do you want to do, or why would
> you want to do that.

From: http://en.wikipedia.org/wiki/Rounding :
Round half to even
A tie-breaking rule that is less biased is round half to even, namely:
If the fraction of y is 0.5, then q is the even integer nearest to y.
Thus, for example, +23.5 becomes +24, as does +24.5; while −23.5 becomes
−24, as does −24.5.
This method treats positive and negative values symmetrically, and is
therefore free of sign bias. More importantly, for reasonable
distributions of y values, the expected (average) value of the rounded
numbers is the same as that of the original numbers. However, this rule
will introduce a towards-zero bias for even numbers, and a
towards-infinity bias for odd ones.

> You could try dividing the number by two, rounding, and multiplying by
> two again. This should give you the results you want.
> 
> irb(main):014:0> ( 8.5 /2).round(0)*2
> => 8
> irb(main):015:0> ( 7.5 /2).round(0)*2
> => 8
> irb(main):016:0> ( 1.0345 /2).round(3)*2
> => 1.034
> irb(main):017:0> ( 1.0335 /2).round(3)*2
> => 1.034
> irb(main):018:0> ( 1.0355 /2).round(3)*2
> => 1.036
> irb(main):019:0> ( 1.0354 /2).round(3)*2
> => 1.036

Great, but: this can go wrong, too:

>> (6.94/2).round(1)*2
=> 7.0
>> (6.93/2).round(1)*2
=> 7.0

The point is that I want unbiased rounding of values that are resulting
from physical measurements; when you can read a measure to 1 decimal,
say 105.5, 104.7, 105.1, 104.9, 104.5, et cetera, and you round these
values to 0 decimals the standard ruby way, then all values ending in .5
will be rounded up; this causes a bias in the average, since actually
chances are equal that 104.5 is either 104 or 105. One way to prevent
this bias is by rounding to the nearest even digit.

-- 
Wybo