ASTM is American Society for Testing and Materials. It is an international
standards organization that develops and publishes voluntary consensus
technical standards
http://www.astm.org/
Rounding (as opposed to truncation in the misleadingly named ROUNDDOWN and
ROUNDUP functions) is generally understood to mean replacing a number by the
nearest number with the rounded precision. This is only ambiguous in the
case of ties. The method I was taught in grade school handled ties by always
rounding them up (as the worksheet ROUND function does). One could as easily
round all ties down. Either way, this type of rounding introduces a bias,
since ties always round in a single direction.
That bias can be reduced/eliminated by handling ties in a way that rounds in
each direction roughly half of the time. The most common way to accomplish
this is to require that the last digit of the rounded number be even in the
case of ties.
http://en.wikipedia.org/wiki/Rounding#Round-to-even_method
This approach has been in the literature for at least a century. It has
been an ASTM standard since 1940. It has been common practice in data
analysis at least since the 1940’s. Almost all standards bodies that bother
to specify how to round recommend it, and IEEE 754 specifies the binary
equivalent for hardware and software arithmetic. Microsoft calls this
"banker's rounding" for reasons that are mysterious to me, since finance is
about the only field where its use is not common.
Jerry
