What is the most reasonable method to round equidistant numbers? At school we were taught that (+/-)0.5 goes to nearest "higher" number or "round half away from zero".
That is 0.5 -> 1 and -0.5 -> -1.

While that looks nice and all (five goes to ten regardless of a sign), the more you think about it, the less it makes sense. Then when you actually start implementing some calculations with rounding in a programming language, you soon discover that every library does it differently.
The various rounding methods


My question is/are:
What is the most reasonable method for rounding with perfectly random distribution and without any preference?
This means I don't get more positive/negative, odd/even numbers. And I don't need to adjust rounding for a special use case such as finance, engineering, etc.
How do mathematicians round equidistant numbers in practice?
Is there some well accepted international standard for this?

images:
https://en.wikipedia.org/wiki/Rounding
https://www.mathsisfun.com/numbers/rounding-methods.html
 A: Let $\mathbb Z=\{\ldots-2,-1,0,1,2,\ldots\}$ be the set of integers.
Let $\frac12\mathbb Z = \{\ldots-2,-\frac32,-1,-\frac12,0,\frac12,1,\frac32,2,\ldots\}$ be the set of integers and half-integers.
In this domain, a rounding function is a function $f:\frac12\mathbb Z\to\mathbb Z$ such that $f(n)=n$ when $n$ is an integer, and $f(x)=x\pm\frac12$ otherwise.
You are asking for a rounding function $f$ that has the following additional properties:

*

*(No preference for particular numbers) For all $n$, the number of $x\in \frac12\mathbb Z$ such that $f(x)=n$ is a constant that does not depend on $n$. (This constant must be $2$.)

*(No preference for positive/negative) If $f(x)=0$ then $f(-x)=0$.

These properties are incompatible with each other!

*

*Property (1) requires that there are exactly two values in $\frac12\mathbb Z$ that round to $0$: either $\{-\frac12, 0\}$ or $\{0,\frac12\}$.

*But property (2) requires that an odd number of values in $\frac12\mathbb Z$ round to $0$: either $\{0\}$ or $\{-\frac12,0,\frac12\}$.

We conclude that an unbiased rounding function meeting the above criteria does not exist. As a result, the appropriate rounding function to use for a given application depends on the particular demands of the application.
