# 2 - Bar Length Measurements 25 Mean = 152.1 mm Number of...

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1 Measurements from first lecture 151 151.2 151.4 151.6 151.8 152 152.2 152.4 152.6 152.8 153 0 5 10 15 20 25 Length of bar (mm) Number of measurements Bar Length Measurements Mean = 152.1 mm Std. dev = 0.34 mm Significant Figures • How to report on the results of a set of measurements? – There are different conventions. We’ll use the convention • RESULT (i.e. Mean) ± STAT ERROR ± SYST ERROR – For our ruler measurement we would report – Length = 152.1 ± 0.3 STAT mm – Or possibly Length = 152.1 ± 0.3 STAT -0 .1 SYST mm if we had some reason to suspect that our rulers were 0.1 mm too long • The sample standard deviation is a measure of the precision of the measurement and quoting the std. dev. is a concise way to report on the distribution of measurement outcomes The convention is to keep 1 significant figure in the uncertainty/std. dev./error and to round the measurement off to the same decimal place : 152.1 ± 0.3 - 0.1 mm Or equivalently 0.1521 ± 0.0003 - 0.0001 m But never: 152100 ± 300 - 100 μ m which would be reported: (1.521 ± 0.03 - 0.01) x 10 5 μ m Significant Figures • Step one: round off the uncertainty/std. dev./error to 1 sig fig. – There should be only one digit. – E.g. ± 0.356 becomes ± 0.4 • (our convention: fives are rounded up) – 345 becomes 3 x 10 2 • Step two: express the measurement with the same precision – 3.456 ± 0.4 becomes 3.5±0.4 – 34234 ± 3 x 10 2 becomes ( 3.42 ± 0.03 ) x 10

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## This note was uploaded on 12/15/2010 for the course PHYS 257 taught by Professor Dobbs during the Fall '07 term at McGill.

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2 - Bar Length Measurements 25 Mean = 152.1 mm Number of...

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