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Round to even changes the distribution
Authored by: JonathanBoyd on Dec 12, '05 02:50:02PM

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:
f
|
|-------------
|
+------------n
But if you then start rounding them to the nearest even, the distribution changes, so that even numbers are more prevalent:
f
|
|__---__---
|
+------------n
I would have thought that that makes it less accurate and produces a bias by clumping results around even numbers.

I guess that we're looking at it with a different intention behind the numbers. I was thinking about patterns and distributions. If you're looking at adding a long chain of numbers, or calculating a mean, as others have suggested, I concede that round to even is probably going to be better. I probably should have objected to the change in distribution, rather than saying 'bias.'

Incidentally, I don't know if it was intention or not, but saying such phrases as 'Also, I know basic statistics,' 'in elementary school' and 'which is what scientists who wish to have non-biased data would use' comes across as a little condescending, which is rather unnecessary.



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