Physics Lab Experiments by Matthew M. J. French

Author:Matthew M. J. French
Language: eng
Format: epub, mobi
ISBN: 9781942270805
Publisher: Mercury Learning and Information
Published: 2016-08-12T04:00:00+00:00

4.13 ESTIMATION OF ERRORS

It often occurs that repeated measurements of a simple quantity like the length of a pendulum gives very little meaningful spread in the results or even the same results each time. In this case calculation of the standard error on a single reading and the standard error in the mean, as described above, is rather meaningless: the accuracy of the measurement is limited by the resolution of the ruler. For example consider using a meter rule with a resolution of 1 cm: that is it has markings every one centimeter. Each time the length is measured the scale is read to the nearest centimeter, so 35.6 would be read as 36. This has introduced a systematic error for this individual reading, but the error in a group of readings is random because it is equally likely to be positive as negative. The error will range from nothing to half a division (0.5 cm), and so the average error will be about a quarter of a division (0.25 cm). The standard error (corresponding to 1 standard deviation if we assume a normal distribution) will be about a third of a division (0.33 cm). Care must be taken to give a reasonable estimate of the error in measurements like this.

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