roy@phri.UUCP (Roy Smith) (08/14/85)
> 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. 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. -- Roy Smith <allegra!phri!roy> System Administrator, Public Health Research Institute 455 First Avenue, New York, NY 10016
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (08/18/85)
> > 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).
sgb@mulga.OZ (Steven Bird) (08/19/85)
> 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. Getting even more off the point, suppose we were to compute 3*4 in base 12. The answer of course is 10(base 12) which has 1 significant figure as required. 10(base 12) translates to 12 +/- 6 (base 10) which I think is more acceptable than the 10 +/- 5 implied by 1 * 10^1 metres^2 above. Error analysis should be *independent* of the base used to represent numbers. For this reason I think there is something fundamentally wrong with the use of significant figures to express accuracy. -- Steven Bird. PHONE: +613 344-5229 (03 344-5229) UUCP: {seismo,ukc}!munnari!sgb mulga!sgb@decvax.uucp
meister@linus.UUCP (Phillip W. Servita) (08/20/85)
In article <402@phri.UUCP> roy@phri.UUCP (Roy Smith) writes: > 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. When my high school physics teacher asked this (actually, the figures were different, but the question the same) question, and then told us the "correct" answer, i said: "BULL PATTIES!!!" this was 4 years ago, as a high school junior. If i was asked the same question now, however, I WOULD STILL SAY 12 METERS SQUARE. And when i would get the "correct answer" in return, I WOULD STILL SAY "BULL PATTIES!!!". Sorry, significant figures freaks, but the question "Whats the area of a table 3 meters wide by 4 meters long" is totally theoretical in nature. You have GIVEN me a table 3 by 4. i dont know how or care how you measured it, you have GIVEN me a table 3 by 4. and GIVEN: a table 3 x 4 meters THEN: that table has an area of 12 meters square. PERIOD. To illustrate this further, let me ask two other questions: 1) (the math majors question) What is the area of a two dimensional rectangular pink elephant 3 meters wide by 4 meters long? 2) (what the physics and sig figs people SHOULD ask) Using a stick ruled only in meters, i measured a table to be about 3 meters wide by 4 meters long. What is its area? (correct answer about 10 meters square) you were right with your 12 meters square answer. -phil
jim@cadomin.UUCP (Jim Easton) (08/22/85)
In reply to Phillip W. Servita I quote out of your posting; > .............. If i was asked the same question now, however, I WOULD STILL > SAY 12 METERS SQUARE. ... and you would be wrong. The correct answer is 12 square meters - the unit is square meters. 12 meters square implies a square which is 12 meters on a side, having an area of 144 square meters. Jim Easton (...!alberta!jim)
jim@cadomin.UUCP (Jim Easton) (08/23/85)
In reply to Phillip W. Servita I quote out of your posting; > .............. If i was asked the same question now, however, I WOULD STILL > SAY 12 METERS SQUARE. ... I would expect an answer of 12 square meters - the unit is square meters. To me 12 meters square implies a square which is 12 meters on a side, having an area of 144 square meters. Jim Easton (...!alberta!jim)
thomas@utah-gr.UUCP (Spencer W. Thomas) (08/24/85)
In article <509@linus.UUCP> meister@linus.UUCP (Philip W. Servita) writes: (various expletives deleted) > GIVEN: a table 3 x 4 meters > > THEN: that table has an area of 12 meters square. PERIOD. the number "3" used in a measurement context (rather than 3.0 or 3.000) means "3 +/- 0.5" Multiplying out the limit cases, we get that the area of the table is between 2.5x3.5 = 8.75 and 3.5x4.5 = 15.75 or approximately 1e1. Saying "3" instead of "3 +/- 0.5" is a convenient shorthand. While mathematically 3x4 is 12, when dealing with measurements you must ALWAYS consider the precision. > >2) (what the physics and sig figs people SHOULD ask) > > Using a stick ruled only in meters, i measured a table to be about > 3 meters wide by 4 meters long. What is its area? (correct answer > about 10 meters square) This is exactly what a measurement type means when he (or she) says the table is "3 meters by 4 meters". Again, it's a shorthand (or jargon) that you learn to understand when you enter the field (just like Kb and the like in CS). -- =Spencer ({ihnp4,decvax}!utah-cs!thomas, thomas@utah-cs.ARPA) "To feel at home, stay at home. A foreign country is not designed to make [one] comfortable. It's designed to make its own people comfortable." Clifton Fadiman
mvr@mimir.dmt.oz (Vaughan Roberts) (08/28/85)
s ie
1) A table 3.5 meters by 4.5 meters we get an answer 15.75 m^2 or
to 1 digit 2 * 10^1 m^2.
2) A table 2.5 meters by 3.5 meters gives 8.75 m^2 or 1 * 10^1 m^2.
The real answer is to do a full error analysis which requires the
uncertainty of the initial measurements to be stated. Without that it is
just pointless hot air to talk of "correct" answers as above.
--
Vaughan Roberts, CSIRO Div of ManTech, Melbourne, Australia.
ACSNET: mvr@mimir.dmt.oz Ph: +61 (03)418-0260
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ARPA: mvr%mimir.dmt.oz@seismo.arpa