
Regarding Calculator and low precision values
If it's calculating significant digits,
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
Regarding Calculator and low precision values
What they teach kids in school is a lie. Rounding 5 up produces a bias, because 5 is exactly in the middle. What you should do is round 5 up half the time, and down the other half. IEEE 754 floating point defines a round to even to do this exactly, so Calculator is correct.
Regarding Calculator and low precision values
But doesn't that produce a bias towards even numbers?
Regarding Calculator and low precision values
Whether a number is odd or even is usually not as important as the magnitude of the error. For example, 5.5+3.5+2.5=11. If we round 5 up, we get 6+4+3=13. If we round to even, we get 6+4+2=12. The effect only appears on longer chains of numbers, where the bias of 5 adds up.
Regarding Calculator and low precision values
Under what conditions would you conceivably care about a bias towards even numbers? The main issue is usually whether some measure, the mean for example, becomes biased by rounding. That's what roundtoeven is for.
Regarding Calculator and low precision values
The bias to even numbers would change the shape of the distribution.
The distribution only matters if
you're doing statistics. If you're doing any other branch of math you want to minimize the total error  the distribution is irrelevant.
Rounding towards even minimizes the total error and is the mechanism used internally by most math chips, IIRC. Here's a link that refers to both methods as "equally valid". 
Regarding Calculator and low precision values
Sorry to correct you, but you are wrong.
Regarding Calculator and low precision values
No, thats wrong. If 2 figures are significant, those two figures are exact.
Regarding Calculator and low precision values
I'm sorry, but the site you linked is incomplete.
Regarding Calculator and low precision values
In trying out a few calculations, Calculator.app does not correctly implement "precision" to mean significant figures either. For example, with precision set at 2:
10,000.00 + 2,500.00 = 12,500 5.25 * 3.00 = 15.75 Further, if you set precision to 2 and type 15.75, the calculator converts the displayed value to 16. It does, however, return the correct value in the following calculation: 15.75 / 3.00 = 5.25 Sadly, this is just an artefact of the way it understands "precision". For the following operation returns the incorrect answer: 15.75 / 3 = 5.25 Ultimately, however, rules for significant figures don't allow you to specify the number you would like. They are based on the precision of the values used in the calculation. Thus, it would be strange if the Calculator.app were using "Precision" to mean significant figures. Best, darin
Rounding Rules
"Five rounds up" is not the only rounding rule  and in my work it is seldom the best.
My concern is that the total (or average) of rounded numbers shouldn't be biased up or down from the originals. (The total of a column of numbers versus the total of the rounded numbers will be exactly equal only by 1in10 chance, but you don't want to do anything so that you expect the total to be consistently higher (or lower) than the originals. To see the bias, think of rounding 1digit numbers. Obviously, 12.0 "rounds" to 12 with no bias. Then "pair up" 12.1 with 11.9  the 0.1 error introduced by rounding one cancels the negative 0.1 of the other. Ditto 12.2 with 11.8, 12.3 with 11.7 and 12.4 with 11.6. But now... 12.5 with 11.5? Yes! The point five is just as close to either integer, so you pick up sometimes and down sometimes (and therefore, round without making the total or expected result always bigger or smaller). The bestknown way is to round to the nearest even number when you have a point 5. 12.5 rounds to 12, as does 11.5. 73.5 and 74.5 both round to 74. If point 5 always rounds up, here's the bias: nine numbers out of ten have no net up or downbias, but one number out of 10 (the ones that end in point 5) rounds to a result that's 0.5 bigger than the source, for an expected increase of 0.05. "Round to nearest/even" introduces no bias. For jumping more than one decimal at a time, the rule is that only point 5000000... gets the "to even" handling. 12.5002 rounds to 13. 12.4998 rounds down to 12. I used Excel to create 3000 random numbers between 0 and 100, then rounded them to one digit (with Excel's ROUND function, which rounds fives up). The total of the original and rounded column was close  just a difference of 1.01 out of 151,829. That's what you expect when you're scrapping about 15 decimal places all at once  the rounding rule hardly matters. But then I rounded the singledecimalplace numbers to zero places, and the total of those grew by 153.9  essentially, the expected 0.05 average bias per number. Rounding to nearest/even works especially well when multiple rounding is applied. If you repeat "five rounds up," knocking off one digit at a time, the typical bias will be almost 0.1, twice the 0.05 I mentioned above. BTW, the IEEE, which sets standards for math on CPU's etc., lists 4 rounding modes. Round to nearest/even is the default for X86 and PPC  probably, for most applications. There are thorny issues about some types of binary calculations but my description is fine for byhand work and should match what you see from most programs that (stupidly) try to outsmart their CPU's. (This is only one of a long list of Excel's dumb math handling.))
Rounding Rules
Rounding away from zero, which is what rounding up usually is, should have no net effect on the mean if you have both positive and negative numbers. If you're only using one of those though, then rounding to even certainly seems to be a better way to get the mean.
Rounding Rules
I can't imagine many common problems where the median value is zero. 
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