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From: gwyn@brl-tgr.ARPA (Doug Gwyn )
Newsgroups: net.med,net.math
Subject: Re: The Perils of Nutrasweet: digits of precision
Message-ID: <777@brl-tgr.ARPA>
Date: Sun, 18-Aug-85 13:36:29 EDT
Article-I.D.: brl-tgr.777
Posted: Sun Aug 18 13:36:29 1985
Date-Received: Tue, 20-Aug-85 21:35:17 EDT
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Organization: Ballistic Research Lab
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Xref: watmath net.med:2111 net.math:2187

> > The usual method of writing numbers (e.g. 10, .007) carries no information
> > about accuracy.  .007 could be accurate to one, two or three decimal places.

The usual convention is to show accuracy past the last significant digit
by postpending zeroes.  0.007 is presumed to be accurate to + or - 0.0005
otherwise.  10 is presumed to have 1 significant digit but 10. indicates
two significant digits.  Real measurement accuracy should not be expressed
in such terms but should have the standard error given also.

> 	This is getting rather off the point, but some of you might like
> this.  During one of my interviews for college, I was asked a typical
> stupid interview question: "What's the area of a table 3 meters wide by 4
> meters long?"  I poked around with various counter-probes like, "Do you
> mean the area of just the top surface, or the top and bottom combined?" and
> then came up with the obvious answer; 12 meters^2.

> 	Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2;
> since the initial data only had 1 digit of accuracy, that's all the final
> answer can have.

This is a typical, but incorrect analysis.  The number of significant digits
in a computed quantity cannot be accurately estimated by any such simple rule.
Assuming that the dimensions of the table were given only to the nearest meter
(which is improbable), range arithmetic should be used, which means
multiplying two rectangular distributions.  If the input quantities had been
assumed to follow a more Gaussian distribution, the best estimate of the area
would be near 12 (with a very considerable standard deviation).