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NNTP-Posting-Date: Mon, 01 Aug 2005 01:50:21 -0500
From: tmoran@acm.org
Newsgroups: comp.lang.ada
Subject: Re: OT: definition of "significant figures"
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Date: Mon, 01 Aug 2005 01:50:21 -0500
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Date: 2005-08-01T01:50:21-05:00
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I think a better formula for the number of digits to display is
   Digit_Count := Integer(Long_Float'ceiling(Log(Abs(Avg),10.0)))
                  -Integer(Log(Sd,10.0));
where the positive addition to the digits comes from a 'ceiling on
log(avg), but a subtraction from the number of digits comes from a
rounded value of log(sd)
  Using this formula, one gets
>         The average of 2.1, 33.1, 2.2
avg = 12.46666, sd =  16.24
    log(avg) = 1.096, 'ceiling = 2
    log(sd)  =-1.211, rounded  = 1
so the digit count is 1, rather than log(avg/sd)= -0.1
  If you don't use the 'ceiling, consider the case where the x(i) are
in the range 99.990 .. 99.999, vs the same set with .01 added, so
their range is 100.000 .. 100.009   Since their std devs are the same,
in the .00x range, their averages ought to be represented with the same
number of digits to the right of the decimal.  The 100's shouldn't
lose a digit compared to the 9's.