FWIW, the method advocated by the OP has been an ASTM standard for about 65
years, and is also specified by almost every other technical standards body
that gives a standard for rounding.
As a matter of historical interest,
1. I would greatly appreciate any information on how this came to be called
"bankers' rounding", since I have seen no evidence that bankers have ever
used it.
2. I would greatly appreciate any pre-1940's references to this method of
rounding. The only early reference that I have been able to nail down is the
1906 4th edition of Robert Woodward's "Probability & Theory of Errors" where
a statement on p.42 suggests that it was standard practice in the preparation
of numerical tables.
Jerry
"JE McGimpsey" wrote:
There is no single "proper" way to round - the best unbiased method
depends on the distribution of numbers rounded.
For instance, if the method you suggested were employed, using =ROUND(x,
0) on a series that produced values on the interval (0, 1), say, the
result would be biased toward zero just as much as XL's ROUND() biases
toward 1. The "proper" method in that case would be to randomly or
alternately bias up and down.
However, to change the method used by XL's ROUND() now would break
existing workbooks that account for that method's bias.
See
http://support.microsoft.com/kb/196652/en-us
Note that VBA uses your method, which MS calls "Banker's Rounding"
In article ,
HAH wrote:
The proper way to round a number ending in 5 with nothing past it to the
previous digit is to round that digit to the nearest even number. Excel
doesn't do that; it uses the obsolete theory that always rounds up so 2.5,
which should round to 2, is being rounded to 3. This means that over time,
in financial uses, money will eventually be over-reported, and in scientific
uses, the amount of energy and matter will eventually be over-reported.
Current rounding theory is to round to the nearest even number so that,
statistically, half the time numbers will be rounded up and half the time
they will be rounded down, thus eliminating artificially high compounded
results.