NATIONAL QUALIFICATIONS CURRICULUM SUPPORT
Physics
Uncertainties
[ADVANCED HIGHER]
N E Fancey
University of Edinburgh
G Millar
Daniel Stewart’s and Melville College, Edinburgh
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This publication deals with the interpretation of experimental data and
with calculations of uncertainties at a level appropriate to practical and
investigation work for the Higher and Advanced Higher in Physics.
It has been prepared by Dr N E Fancey, University of Edinburgh and
Mr G Millar, Daniel Stewart’s and Melville College, Edinburgh. It is based
on Memorandum No 65, Uncertainties in Experimental Work, by Dr E M
Wray, University of St Andrews.
First published 2000
Electronic version 2001
© Learning and Teaching Scotland 2000
This publication may be reproduced in whole or in part for educational purposes by
educational establishments in Scotland provided that no profit accrues at any stage.
Acknowledgement
Learning and Teaching Scotland gratefully acknowledge this contribution to the Higher
Still support programme for Physics. The authors and publisher record their thanks to
Mary Webster, Development Officer for Higher Still Physics, for editorial work on this
publication.
ISBN 1 85955 870 4
Learning and Teaching Scotland
Gardyne Road
Dundee
DD5 1NY
www.LTScotland.com
CONTENTS
Introduction
Part One:
Part Two:
1.
2.
3.
4.
1
5.
6.
7.
8.
9.
Accuracy of measurements and uncertainties
Significant figures and scientific notation
Errors and uncertainties
Scientific notation, units and multiples of units and
significant figures
How uncertainties arise in experiments
A closer look at uncertainty
Combining uncertainties
Uncertainty calculation
Graphical methods
6
6
9
10
14
18
10.
11.
12.
13.
14.
15.
Use of graphs and spreadsheets
Graphing results with the EXCEL spreadsheet
Uncertainties in gradient and intercept
Note on LINEST
Data handling with a spreadsheet
Comparison of results
23
24
25
25
28
30
Part Three: 16.
17.
18.
19.
Populations, samples and distributions
The mathematics of distributions
The normal distribution
Uncertainties in combinations and functions of
variables
20. Uncertainties in experiments on radioactivity
21. Straight-line fitting with calculators
3
3
5
33
34
35
38
40
42
References: Further reading, other references, websites
45
Appendix 1: Units, prefixes and scientific notation
47
Appendix 2: Calibration uncertainties in instruments
49
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