To say "NO!" is a bit emphatic, since I could just as well say that we
will only truncate numbers, which would provide an answer which may be
fine for some conditions.

I understand your logic; but this is still including 500 numbers below
the "rounded to" value and 499 above, therefore (and I repeat)
statistically, you are favoring the round up when given a random set of
values.

  Again looking at the results of the scenario I presented below,
The actual answer is                 2260 +/- 10

The "Round >=5" result is            2270  (+0/-20)
The "Round Even if 5" result is      2260  (+/- 10)
And the "Truncate" result is         2250  (+20/-0)

So which answer is right?
   All of them (or none of them) depending on the requirements...

David W. Gulley
Destiny Designs


Kevin Brain wrote:
>
> NO! becasue 1000 is the same as 0. Er - that needs explaining! i.e. there
> are 500 numbers 0-499 inclusive and 500 numbers 500-999 inclusive. So the
> 1000 is the 0 in the next set.
>
> Regards, Kevin
>
> ----- Original Message -----
> From: "David W. Gulley" <dgulley@DESTINYDESIGNS.COM>
> To: <PICLIST@MITVMA.MIT.EDU>
> Sent: Thursday, May 31, 2001 3:30 PM
> Subject: Re: [OT]: Brain Burp Rounding??
>
> > Roman Black wrote:
> > >
> > > Hi Michael, yep, darn right, half the people in
> > > the world (including me!) have been rounding wrongly
> > > their entire lives. Very scary. There is and can only
> > > be one correct way of rounding decimal numbers...
> > >
> > > Here is an example, assuming rounding to 3 decimal
> > > places, that is 1000 combinations, from 000 to 999.
> > >
> > > 000 to 499 (first half), 500 to 999 (second half).
> > > There are the first 500 combinations in the first
> > > half, and the second 500 combination in the second
> > > half.
> > >
> > > All my life I have been rounding at 555, under the
> > > false impression that 5 is "half way" in decimal
> > > terms... Wow.
> > >
> > > I asked my 26 yr old science-degreed girlfriend how
> > > to round and she looked at me like I was stupid.
> > > "5 or more, round up". She was taught correctly.
> > >
> > > Now I'm wondering if it is mainly us old-timers
> > > from the dawn of pocket calculators age that were
> > > taught wrong?? Any thoughts, older people??
> > > :o)
> > > -Roman
> >
> > Cept for one minor detail,
> >
> > There are 999 values BETWEEN 0 and 1000.
> >    500 IS the halfway point.
> >      500 values below it (0 - 499) and
> >      500 values above it (501 - 1000).
> >  Therefore, if accumulating a large series of "random" numbers and
> > rounding using the 5 or greater rule, the result will "tend" to be too
> > large since statistically you are using 500 possibilities below the
> > number and 499 above the number.
> >
> > For most things this error would probably not be a problem, but the
> > "round to even if 5" rule will "tend" to average out the error
> > accumulation at the expense of complicating the rule slightly.
> >
> > The validity of the least significant digits does play an important role
> > in the process, so when absolute accuracy is required use a tolerance
> > (+/-) to exactly specify the values, and the error accumulation.
> >   For example (round to nearest 1/100):
> >     Value   Tolerance    Round >=5     Round to Even if 5
> >     1.125   +/- 0.005      1.13          1.12
> >     1.135   +/- 0.005      1.14          1.14
> >      Repeat above 1000 times and Total
> >     2260                   2270          2260
> >
> > when the tolerances say:
> >     2260 +/- 10 or somewhere in the range of 2250 to 2270 so yes the
> > "Round >=5" is a 'correct' answer (since it is in the possible range
> > defined by the tolerances, even if it is at the upper limit), but the
> > 2260 provided by the "Round to even if 5" is a 'better' answer (in some
> > cases).
> >
> >   Obviously this is a contrived scenerio, but if a particular sensor
> > reported to 0.5 units of precision with +/- 0.5 units of accuracy, and
> > you wanted to accumulate readings over a long interval, the "Round >=5"
> > will provide an answer that is "typically" too large.
> >
> > If you were buying gasoline, and the pumps all rounded using the "Round
> > >=5" rule, would you mind that you were charged for 2270 gallons instead
> of 2260? :-)
> >
> > As I stated in an earlier message in this thread,
> >     This is a very debatable subject!
> >
> >
> > David W. Gulley
> > Destiny Designs

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