Editing Rounding (section)

====Rounding half to even====
One may also '''round half to even''', a tie-breaking rule without positive/negative bias ''and'' without bias toward/away from zero. By this convention, if the fractional part of {{mvar|x}} is 0.5, then {{mvar|y}} is the even integer nearest to {{mvar|x}}. Thus, for example, 23.5 becomes 24, as does 24.5; however, −23.5 becomes −24, as does −24.5. This function minimizes the expected error when summing over rounded figures, even when the inputs are mostly positive or mostly negative, provided they are neither mostly even nor mostly odd.

This variant of the round-to-nearest method is also called '''convergent rounding''', '''statistician's rounding''', '''Dutch rounding''', '''Gaussian rounding''', '''odd–even rounding''',<ref>[https://web.archive.org/web/20150603082624/http://mscweb.gsfc.nasa.gov/543web/files/GSFC-X-673-64-1F.pdf Engineering Drafting Standards Manual] (NASA), X-673-64-1F, p90</ref> or '''bankers' rounding'''.<ref>{{cite book |title=Postcards 4 Language Booster: Workbook with Grammar Builder |last1=Abbs |first1=Brian |last2=Barker |first2=Chris |last3=Freebairn |first3=Ingrid |publisher=Pearson Education |year=2003 |isbn=0-13-093904-8 |at=[https://books.google.com/books?id=mpvSnBZTsOgC&dq=%22bankers%20rounding%22&pg=PA85 {{pgs|85}}] |quote=Rounding to the nearest even number is also called 'bankers rounding' because the banks use this technique as well.}} {{pb}} {{cite book |publisher=Microsoft Corporation |title=Microsoft Pascal Compiler for the MS-DOS Operating System User's Guide |year=1985 |at=[https://archive.org/details/microsoft-pascal-3.30-users-guide/page/165/ {{pgs|165}}] |quote=Bankers' rounding is used when truncating real numbers that end with .5; that is, odd numbers are rounded up to an even integer, even numbers are rounded down to an even integer.}}</ref>

This is the default rounding mode used in [[IEEE 754]] operations for results in binary floating-point formats.

By eliminating bias, repeated addition or subtraction of independent numbers, as in a [[Random walk#One-dimensional random walk|one-dimensional random walk]], will give a rounded result with an error that tends to grow in proportion to the square root of the number of operations rather than linearly.

However, this rule distorts the distribution by increasing the probability of evens relative to odds. Typically this is less important{{citation needed|date=December 2021}} than the biases that are eliminated by this method.