Roundig to nearest 10
Tim Murray
say you were asked to round to the nearest ten, as in 0, 10, 20...
Would 4.9 round to zero, or would it round to 10? Some say 10, because 4.9
rounds to 5 then 5 rounds to 10. I say it rounds to zero: I look like like a
ruler. Once you reach 5 you round to 10, but until then, you're at zero.
bert
The informed view is generally that rounding
after rounding is a source of bias, so you
should only round once.
Another informed view is that round-to-even
in the case of a tie is less biased than
rounding up or rounding down. Thus, you
should round 5 down to 0, 15 up to 20,
25 down to 20, and 35 up to 40.
--
Arturo Magidin
> No one argue that 4.9 would not round to 5, when rounding to an integer. But
> say you were asked to round to the nearest ten, as in 0, 10, 20...
>
> Would 4.9 round to zero, or would it round to 10?
Zero.
> Some say 10, because 4.9
> rounds to 5 then 5 rounds to 10.
Then they would not be following the usual rules of "rounding". While
whether the precise midpoint rounds up or down is up for grabs,
anything less than the midpoint definitely rounds down. That's why
0.49 would round to 0, not to 1 (as it happens in countries that have
eliminated cent coins).
> I say it rounds to zero: I look like like a
> ruler. Once you reach 5 you round to 10, but until then, you're at zero.
"Rounding to the nearest 10" is the same as first dividing by 10, then
rounding as usual, and then multiplying by 10. So you would take 4.9,
divide by 10 to get 0.49; then round as usual to get 0, then multiply
by 10 to get 0.
Who is it you believe claims that 0.49 rounds to 1?
--
Arturo Magidin
Tim Murray
> Who is it you believe claims that 0.49 rounds to 1?
It was a usenet argument. I posted here because I wanted to make sure I had
some ammo before I launched got into the debate. However, after posting here
I went back and read his post again, and turns out he would have rounded to
zero as well.
Tim Murray
> Another informed view is that round-to-even
> in the case of a tie is less biased than
> rounding up or rounding down. Thus, you
> should round 5 down to 0, 15 up to 20,
> 25 down to 20, and 35 up to 40.
I've never heard of that. What is its basis? And why even? Why not odd? The
reason why I asked why not odd is because I read somewhere of there being one
more even number integers than odds in the universe -- the special zero.
Arturo Magidin
Nonsense. The set of even integers is equinumerous to the set of odd
numbers. And the density of each is 1/2.
--
Arturo Magidin
bert
Well, I suppose that round-to-odd in the case
of a tie would be as unbiased as round-to-even,
but I've never seen it suggested, while I've
seen round-to-even recommended quite often -
and especially in the IEEE 754 floating point
standard, which was the outcome of an enormous
amount of precise and painstaking investigation.
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