
Regarding Calculator and low precision values
Yeah, that's the problem.
Regarding Calculator and low precision values
Actually, the rules for rounding say that you round a number ending in 5 to the *even* number. So,
Regarding Calculator and low precision values
Having spent several years studying physics, I can reliably inform you that the proper scientific practice is to round 5s up every time. Always rounding to even numbers produces a bias towards them and brings in an additional inaccuracy.
Regarding Calculator and low precision values
I wouldn't use "proper scientific practice", I would rather use "force of habit" or more bluntly "inertia". None of the various research/lecturing colleages (in Physic, Maths, Biology) whom, ages ago, I asked why one rounds up on a 5 has been able to give any other answer than "because everybody else does so"...
The "round to even" does NOT produce a bias
"Having spent several years studying physics..." Well, I have a degree in physics (Bachelor, and some graduate school work towards Physics PhD). Also, I know basic statistics.
"Always rounding to even numbers produces a bias towards them and brings in an additional inaccuracy." The only way you can say that is if you know that your original numbers (to some chosen significance) tend to be odd. Do they? No, they do not. On average, you are just as likely to get even numbers as you are to get odd numbers for a given range of possibilities. Thus, if you then follow the rule to "round to nearest even for numbers EXACTLY between two digits" you will NOT have a bias. If you instead do as suggested here (and in elementary school) and round upwards, you will absolutely introduce a bias to larger values in your data. For more, read the Wikipedia entry (look under Statistician's Method, which is what scientists who wish to have nonbiased data would use): http://en.wikipedia.org/wiki/Rounding (note the phrase "This method is sometimes known as "round to even" and is used in order to eliminate the bias that would come from always rounding a number ending in five up every time." in particular.)
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 04 rounding down and 59 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.
Round to even changes the distribution
To be honest, I don't trust Wikipedia to be terribly accurate, so I went and tried a few more trustworthy mathematical sites and they seem to say the same thing. I must confess that I'm quite surprised by that. If you take a distribution of random numbers, it should be fairly flat:
Regarding Calculator and low precision values
As I stated in another post for this article: Under what conditions would you conceivably care about a biastoevennumbers in a dataset? (I might; I deal with spatial statistics and ordering, but most people? I doubt it.)
That's news to me
I was about to respond just as Jonathan did, but while Googling for corroborative evidence, I found this page, which at the bottom has a rule that supports what Darin is stating.
Forgot to set HTML
I meant to give a link to this page

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