NATIONAL QUALIFICATIONS CURRICULUM SUPPORT Physics Uncertainties [ADVANCED HIGHER] N E Fancey University of Edinburgh G Millar Daniel StewartÂ’s and Melville College, Edinburgh =>? 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 StewartÂ’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 20;51+5 EEE EL 20;51+5