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Re: [Phys-L] rounding



On 08/24/2012 01:44 PM, Robert Cohen asked:

And so the answer is...?

The whole topic of rounding a GPA is nonsense, because GPA does not
mean anything. It cannot possibly mean anything.

Proof:
*) Suppose one physics major chooses an elective "music appreciation"
course (consisting of listening to music and sitting around talking
about it) and gets an A, raising his GPA.
*) Meanwhile another physics major chooses instead the "composition
and orchestration" course (the same course that real musicians take)
and gets a C, lowering his GPA.

Over the years, I have looked at many thousands of transcripts. Which
of these candidates do you think I am going to rank higher (at this
stage of the process) for purposes of grad-school admission ... or a
job offer ... or fellowship money?

Further proof: Even if the courses are nominally the same, suppose
we are comparing a 2.99 GPA from Princeton against a 3.01 GPA from
Wossamotta U.

The idea that anybody would make a decision based on GPA without regard
to the level of the courses or the amount of grade inflation results in
my hair standing on end and purple smoke coming out of my ears.

==================

As an attempt to give an answer of the kind that was expected, suppose
we were talking about some quantity that actually meant something.

Roundoff error is an error. If the requirement is that the score be
greater than or equal to 3, then 2.999998 does not meet the requirement.

It should to without saying that the calculation should be carried out
in such a way that roundoff error does not affect the result. This can
be accomplished in several ways:
a) The most sensible way is to use rational numbers. The numerator
and denominator are integers. If the numerator is less than 3
times the denominator, then the score does not meet the requirement.
Roundoff does not occur, so it is not a problem. Computers are quite
capable of representing rational numbers.
b) If for some reason you insist on using decimals, then carry out
the calculation using enough guard digits to ensure that roundoff
error does not affect the result.

Bottom line: Roundoff error is an error. I would hope that anybody
graduating from college with any GPA whatsoever would know this.