Quantitative Methods for Business Fifth Edition Managers in every organisation use quantitative methods One of their essential skills is the ability to understand numerical information and use it for decision making Not surprisingly, management students a course in quantitative methods, typically with names like quantitative analysis, decision analysis, business modelling or financial methods This book gives an introduction to methods that are widely used in business, which every student of management will meet somewhere in their course Whether you are studying for an HND, a first degree, an MBA or postgraduate degree, or a professional qualification, the book covers key topics in an easy to follow and practical way Quantitative Methods for Business Waters Quantitative Methods for Business, fifth edition, is divided into five parts which develop the subject in a logical sequence • Part One introduces the subject, asks why managers use quantitative methods and reviews essential quantitative tools • Part Two describes data collection and description, showing how to select and present information reliably • Part Three looks at specific types of management problem that are invariably tackled using quantitative methods, such as financial analyses and forecasting • Part Four introduces the ideas of uncertainty, focusing on probabilities, the elements of statistics and sampling • Part Five shows how statistical ideas are used in decision making, quality management, inventory management and other areas Key features • A comprehensive view of quantitative methods actually used by managers • No previous knowledge or experience assumed, enabling you to study at your own pace • The subject is developed in a logical order with a clear and easy to follow style • Worked examples illustrate key principles needed to grasp the subject • ‘Ideas in practice’ and case studies show how methods are actually used • Self-assessment problems, chapter outlines and summaries, review questions, research projects and sources of information help to reinforce learning • Extensive companion website with a range of additional material at www.pearsoned.co.uk/waters Donald Waters is the author of many successful textbooks and is well known for his clarity of style He was a professor of finance and operations management and now works in management analysis, research and education Front cover image: © Getty Images CVR_WATE9470_05_SE_CVR.indd Fifth Edition Quantitative Methods for Business Donald Waters www.pearson-books.com 07/02/2011 10:38 Quantitative Methods for Business Visit the Quantitative Methods for Business, Fifth Edition companion website at www.pearsoned.co.uk/waters to find valuable student learning material including: n n n n n n n n Reviews of important material Data sets for problems, examples and cases in the book Spreadsheet templates for calculations Additional material to extend the coverage of key topics Proofs and derivations of formulae Answers to problems Additional worked examples and case studies A list of useful websites We work with leading authors to develop the strongest educational materials in business, bringing cutting-edge thinking and best learning practice to a global market Under a range of well-known imprints, including Financial Times Prentice Hall, we craft high quality print and electronic publications which help readers to understand and apply their content, whether studying or at work To find out more about the complete range of our publishing please visit us on the World Wide Web at: www.pearsoned.co.uk Quantitative Methods for Business FIFTH EDITION Donald Waters Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk First published 1993 Second edition published under the Addison-Wesley imprint 1997 Third edition 2001 Fourth edition 2008 Fifth edition published 2011 © Pearson Education Limited 1997, 2001 © Donald Waters 2008, 2011 The right of Donald Waters to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners The screenshots in this book are reprinted by permission from Microsoft Corporation ISBN 978-0-273-73947-0 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Waters, C D J (C Donald J.), 1949– Quantitative methods for business / Donald Waters — 5th ed p cm ISBN 978-0-273-73947-0 (pbk.) Industrial management–Mathematical models Decision making– Mathematical models I Title HD30.25.W384 2011 658.4′03–dc21 2011000148 10 15 14 13 12 11 Typeset in 10/12pt Sabon by 35 Printed by Ashford Colour Press Ltd, Gosport TO CHARLES BRIEF CONTENTS Preface Part One – Background Managers and numbers Calculations and equations Drawing graphs Part Two – Collecting and summarising data Collecting data Diagrams for presenting data Using numbers to describe data Describing changes with index numbers xvii 19 50 75 77 103 134 163 Part Three – Solving management problems 183 10 11 Finance and performance Regression and curve fitting Forecasting Linear programming 185 216 249 283 Part Four – Introducing statistics 311 12 13 14 15 313 336 370 392 Uncertainty and probabilities Probability distributions Using samples Testing hypotheses Part Five – Management problems involving uncertainty 421 16 17 18 19 20 423 452 479 504 531 Making decisions Quality management Inventory management Project management Queues and simulation viii Brief contents Glossary Appendices Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Index 555 Solutions to review questions Probabilities for the binomial distribution Probabilities for the Poisson distribution Probabilities for the Normal distribution Probabilities for the t-distribution Critical values for the c2 distribution 567 581 586 590 591 592 594 CONTENTS Preface Part One – Background Managers and numbers Chapter outline Why use numbers? Solving problems Useful software Chapter review Case study – Hamerson and Partners Problems Research projects Sources of information Calculations and equations Chapter outline Working with numbers Changing numbers to letters Solving equations Simultaneous equations Powers and roots Chapter review Case study – The Crown and Anchor Problems Research projects Sources of information Drawing graphs Chapter outline Graphs on Cartesian coordinates Quadratic equations Drawing other graphs Graphs of simultaneous equations Chapter review Case study – McFarlane & Sons Problems Research projects Sources of information xvii 3 12 15 15 16 16 17 19 19 20 27 29 32 36 45 46 46 47 49 50 50 50 58 62 66 70 71 72 73 73 www.downloadslide.com APPENDIX D Probabilities for the Normal distribution z 00 01 02 03 04 05 06 07 08 09 0.0 0.1 0.2 0.3 0.4 5000 4602 4207 3821 3446 4960 4562 4168 3783 3409 4920 4522 4129 3745 3372 4880 4483 4090 3707 3336 4840 4443 4052 3669 3300 4801 4404 4013 3632 3264 4761 4364 3974 3594 3228 4721 4325 3936 3557 3192 4681 4286 3897 3520 3156 4641 4247 3859 3483 3121 0.5 0.6 0.7 0.8 0.9 3085 2743 2420 2119 1841 3050 2709 2389 2090 1814 3015 2676 2358 2061 1788 2981 2643 2327 2033 1762 2946 2611 2296 2005 1736 2912 2578 2266 1977 1711 2877 2546 2236 1949 1685 2843 2514 2206 1922 1660 2810 2483 2177 1894 1635 2776 2451 2148 1867 1611 1.0 1.1 1.2 1.3 1.4 1587 1357 1151 0968 0808 1562 1335 1131 0951 0793 1539 1314 1112 0934 0778 1515 1292 1093 0918 0764 1492 1271 1075 0901 0749 1469 1251 1056 0885 0735 1446 1230 1038 0869 0721 1423 1210 1020 0853 0708 1401 1190 1003 0838 0694 1379 1170 0985 0823 0681 1.5 1.6 1.7 1.8 1.9 0668 0548 0446 0359 0287 0655 0537 0436 0351 0281 0643 0526 0427 0344 0274 0630 0516 0418 0336 0268 0618 0505 0409 0329 0262 0606 0495 0401 0322 0256 0594 0485 0392 0314 0250 0582 0475 0384 0307 0244 0571 0465 0375 0301 0239 0559 0455 0367 0294 0233 2.0 2.1 2.2 2.3 2.4 0228 0179 0139 0107 0082 0222 0174 0136 0104 0080 0217 0170 0132 0102 0078 0212 0166 0129 0099 0075 0207 0162 0125 0096 0073 0202 0158 0122 0094 0072 0197 0154 0119 0091 0069 0192 0150 0116 0089 0068 0188 0146 0113 0087 0066 0183 0143 0110 0084 0064 2.5 2.6 2.7 2.8 2.9 0062 0047 0035 0026 0019 0060 0045 0034 0025 0018 0059 0044 0033 0024 0018 0057 0043 0032 0023 0017 0055 0041 0031 0023 0016 0054 0040 0030 0022 0016 0052 0039 0029 0021 0015 0051 0038 0028 0021 0015 0049 0037 0027 0020 0014 0048 0036 0026 0019 0014 3.0 0013 0013 0013 0012 0012 0011 0011 0011 0010 0010 www.downloadslide.com APPENDIX E Probabilities for the t-distribution Significance level Degrees of freedom 0.25 0.20 0.15 0.10 0.05 0.025 0.01 0.005 1.000 816 765 741 1.376 1.061 978 941 1.963 1.386 1.250 1.190 3.078 1.886 1.638 1.533 6.314 2.920 2.353 2.132 12.706 4.303 3.182 2.776 31.821 6.965 4.541 3.747 63.657 9.925 5.841 4.604 727 718 711 706 703 920 906 896 889 883 1.156 1.134 1.119 1.108 1.100 1.476 1.440 1.415 1.397 1.383 2.015 1.943 1.895 1.860 1.833 2.571 2.447 2.365 2.306 2.262 3.365 3.143 2.998 2.896 2.821 4.032 3.707 3.499 3.355 3.250 10 11 12 13 14 700 697 695 694 692 879 876 873 870 868 1.093 1.088 1.083 1.079 1.076 1.372 1.363 1.356 1.350 1.345 1.812 1.796 1.782 1.771 1.761 2.228 2.201 2.179 2.160 2.145 2.764 2.718 2.681 2.650 2.624 3.169 3.106 3.055 3.012 2.977 15 16 17 18 19 691 690 689 688 688 866 865 863 862 861 1.074 1.071 1.069 1.067 1.066 1.341 1.337 1.333 1.330 1.328 1.753 1.746 1.740 1.734 1.729 2.131 2.120 2.110 2.101 2.093 2.602 2.583 2.567 2.552 2.539 2.947 2.921 2.898 2.878 2.861 20 21 22 23 24 687 686 686 685 685 860 859 858 858 857 1.064 1.063 1.061 1.060 1.059 1.325 1.323 1.321 1.319 1.318 1.725 1.721 1.717 1.714 1.711 2.086 2.080 2.074 2.069 2.064 2.528 2.518 2.508 2.500 2.492 2.845 2.831 2.819 2.807 2.797 25 26 27 28 29 684 684 684 683 683 856 856 855 855 854 1.058 1.058 1.057 1.056 1.055 1.316 1.315 1.314 1.313 1.311 1.708 1.706 1.703 1.701 1.699 2.060 2.056 2.052 2.048 2.045 2.485 2.479 2.473 2.467 2.462 2.787 2.779 2.771 2.763 2.756 30 40 60 120 t 683 681 679 677 674 854 851 848 845 842 1.055 1.050 1.046 1.041 1.036 1.310 1.303 1.296 1.289 1.282 1.697 1.684 1.671 1.658 1.645 2.042 2.021 2.000 1.980 1.960 2.457 2.423 2.390 2.358 2.326 2.750 2.704 2.660 2.617 2.576 www.downloadslide.com APPENDIX F Critical values for the c distribution Significance level Degrees of freedom 0.250 0.100 0.050 1.32 2.77 4.11 5.39 2.71 4.61 6.25 7.78 3.84 5.99 7.81 9.49 6.63 7.84 9.04 10.2 11.4 9.24 10.6 12.0 13.4 14.7 10 11 12 13 14 12.5 13.7 14.8 16.0 17.1 15 16 17 18 19 20 21 22 23 24 0.025 0.010 0.005 0.001 5.02 7.38 9.35 11.1 6.63 9.21 11.3 13.3 7.88 10.6 12.8 14.9 10.8 13.8 16.3 18.5 11.1 12.6 14.1 15.5 16.9 12.8 14.4 16.0 17.5 19.0 15.1 16.8 18.5 20.3 21.7 16.7 18.5 20.3 22.0 23.6 20.5 22.5 24.3 26.1 27.9 16.0 17.3 18.5 19.8 21.1 18.3 19.7 21.0 22.4 23.7 20.5 21.9 23.3 24.7 26.1 23.2 24.7 26.2 27.7 29.1 25.2 26.8 28.3 29.8 31.3 29.6 31.3 32.9 34.5 36.1 18.2 19.4 20.5 21.6 22.7 22.3 23.5 24.8 26.0 27.2 25.0 26.3 27.6 28.9 30.1 27.5 28.8 30.2 31.5 32.9 30.6 32.0 33.4 34.8 36.2 32.8 34.3 35.7 37.2 38.6 37.7 39.3 40.8 42.3 43.8 23.8 24.9 26.0 27.1 28.2 28.4 29.6 30.8 32.0 33.2 31.4 32.7 33.9 35.2 36.4 34.2 35.5 36.8 38.1 39.4 37.6 38.9 40.3 41.6 43.0 40.0 41.4 42.8 44.2 45.6 45.3 46.8 48.3 49.7 51.2 www.downloadslide.com 593 Critical values for the c distribution Significance level Degrees of freedom 0.250 0.100 0.050 0.025 0.010 0.005 0.001 25 26 27 28 29 29.3 30.4 31.5 32.6 33.7 34.4 35.6 36.7 37.9 39.1 37.7 38.9 40.1 41.3 42.6 40.6 41.9 43.2 44.5 45.7 44.3 45.6 47.0 48.3 49.6 46.9 48.3 49.6 51.0 52.3 52.6 54.1 55.5 56.9 58.3 30 40 50 60 70 34.8 45.6 56.3 67.0 77.6 40.3 51.8 63.2 74.4 85.5 43.8 55.8 67.5 79.1 90.5 47.0 59.3 71.4 83.3 95.0 50.9 63.7 76.2 88.4 100 53.7 66.8 79.5 92.0 104 59.7 73.4 86.7 99.6 112 80 90 100 88.1 98.6 109 96.6 108 118 112 123 136 116 128 140 125 137 149 102 113 124 107 118 130 www.downloadslide.com INDEX 80/20, rule of 462, 498 a priori probability 315–16 ABC analysis of stock 498–9 acceptance quality level 467–8 acceptance sampling 464, 465–9 achieved quality 453 acid test 188 activity (in project) 506 critical 514–16 timing 511–20 additive model for forecasting 270, 277–8 aggregate index 172 algebra 27–9 alternative hypothesis 393 annual percentage rate 200 annuities 208–10 appraisal costs 456 arithmetic 20–1 algebra 27–9 order of 20–1 with fractions 22–5 with percentages 24–5 with powers 36–44 with probabilities 317–22 arithmetic mean see mean autocorrelation 238 average arithmetic mean 137–40 choice of measures 145 of grouped data 139–40 mean 137–40 median 141–2 mode 142–4 moving average 260–4, 271 weighted mean 139 axes 51–4, 111–14 bar charts 117–20 base 43 base period 164 changing 169–71 for index 164 weighting 173 base value 164 Bayes’ theorem conditional probabilities 323–8 in decisions 434–6 Bessel’s correction 380–1 bias 90 binomial distribution 341–6 definition 341 mean, etc 344 shape 343–4 tables 581–5 box-and-whisker diagram 147 box plot 147 break-even point 190–7 calculation capacity 186 capital productivity 187 cardinal data 82–3 Cartesian co-ordinates 50–8, 111–14 case study Bremen Engineering 474–5 Consumer Advice Office 159–60 Crown and Anchor, The 46 Elemental Electronics 305–6 Gamblers’ Press, The 332–3 Hamerson and Partners 15 Heinz Muller Engineering 178 High Acclaim Trading 130–1 Kings Fruit Farm 388–9 Machined components 366–7 McFarlane &c Sons 71–2 Natural Wholemeal Biscuits 100 Newisham Reservoir, The 447 OnlineInkCartridges.com 212 Palmer Centre for Alternative Therapy, The 551–2 Templar Manufacturing 501 Western General Hospital 245 Westin Contractors 527 Willingham Consumer Protection Department 416 Workload planning 279–80 causal forecast 225–8, 251 causal relationship 221 cause-and-effect diagrams 463, 464 census 85, 371 www.downloadslide.com Index central limit theorem 373, 381, 523 certainty, decisions under 426–7 change, index numbers 163–78 charts see diagrams Chi-squared distribution critical values 408–10, 592–3 definition 407 goodness of fit 407–10 shape 408 tests of association 412–14 class 106, 109–10 cluster sample 91 coefficient of correlation 231–3 determination 229–30 rank correlation 233–4 skewness 156 variation 155 collecting data 77–100 combinations 338–41 common logarithms 43 common fraction 22–4 compound interest 198–9 conditional probability 323–30, 434 confidence interval 377–82 for means 377–9 one sided 382–4 for proportion 381 small samples 385–7 constant 28 constant series 255 constrained optimisation 283–4 constraints 285–7 in LP graphs 290–6 consumer’s risk 468 contingency table 412–14 continuous data 83 diagrams presenting 124–8 in frequency distribution 109 probability distributions 353–4 control limit 470–2 controlling stock see stock control co-ordinates 50–8, 111–14 correlation coefficient 231–3 rank 233–4 costs break-even analysis 190–7 data collection 79–81 economies of scale 194–5 marginal 196–7 of quality 455–7 in queues 533 in stock control 482–3 covariance 154 criteria for decision making 427–31 critical activities 514–16 critical Chi-squared values 408–10 table 592–3 critical path 514–16 cube root 39 cubic equations 63 cumulative frequency distribution 110 cumulative percentage frequency distribution 110 current-weighted index 173–4 curve fitting 240–3 customer satisfaction 453 cycle service level 492 data amount 79–81 cardinal 82–3 classes 106 definition 78 description 134–60 diagrams 103–31 measures of 134–60 ordinal 82 presentation 103–31 reduction 103–6, 134 sampling 370–419 spread 135–6, 147–54 types 82–4 value of 80–1 data collection 77–100 organisation 92–8 sampling 85–91 decimal fraction 22–4 decimal places 25–6 decimals 22–5 decision criteria 427–31 choice 430–1 Laplace 428 Savage 429–30 Wald 428–9 features 424 map 424–5 node 440 payoff matrix 426 tree 439–45 variable (for LP) 287 decision making 423–51 approach giving structure 424–6 sequential decisions 439–45 with certainty 426–7 with uncertainty 427–31 595 www.downloadslide.com 596 Index degeneracy 304 degrees of freedom in Chi-squared 407–8 in t-distribution 385–7 Delphi method 254 demand Normally distributed 492–4 in stock control 481–2 Demand Forecasting System (DFS) 525 denominator 22 dependent demand 482 dependent events 323 dependent variable 51, 111, 221 depreciation 205–7 describing data by diagrams 103–31 by numbers 134–60 deseasonalising data 263–4, 270, 271–7 designed quality 453 determination, coefficient of 229–30 deterministic situations 314 deviation 149 mean 149–50 mean absolute 149–51 mean squared 151–4 quartile 147–8 see also standard deviation diagrams 103–31 bar charts 117–20 frequency distribution 108–10 Gantt chart 518, 519 graphs 50–72, 111–14 histogram 124–6 Lorenz curve 127–8 network 508–10 ogive 126–7, 142 p-chart 470 pictograms 121–2 pie charts 115–16 scatter diagrams 111–12 tables 106–11 tree decision 439–45 probability 328–30 discount factor 201 discount rate 201 discounting to present value 201–7 discrete data 82–3 diseconomies of scale 195 dispersion see spread distribution free test see non-parametric test distributions, probability 336–69 binomial 341–6, 581–5 Chi-squared 407–10 definition 336 empirical 337 negative exponential 534 Normal 353–65, 590 Poisson 347–52, 586–9 t 385–7 distribution of sample means 372–7 dividend cover 189 dividends per share 189 e see exponential constant earnings per share 189 economic order quantity 484–8 economies of scale 194–5 e-mail survey 94 empirical probability 316 energy productivity 187 equations definition 27 graphs of 50–72 quadratic 58–61 simultaneous 32–6, 66–8 solving 29–32 equipment productivity 187 error in forecasts 256–9 in hypothesis testing 394–5 in regression 217–18 in time series 256–9 measures mean error 219, 257–8 mean absolute error 220, 258 mean squared error 220, 258 estimation of population proportions 381 event dependent 323 independent 317–18 mutually exclusive 319–22 random 347–8 expected value 432–3 exponential constant 43, 64 graphs of 64–5 exponential curves 64–5 exponential function 42–4 exponential smoothing 263, 265–8 external failure costs 456 extrapolation 225 feasible region 292–6 finance 185–214 annuities 208–10 break-even point 190–7 www.downloadslide.com Index depreciation 205–7 discounting to present value 201–7 economies of scale 194–5 interest 197–200 internal rate of return 203–4 measures of performance 185–9 mortgages 208–10 net present value 201–3 sinking fund 208–10 financial ratios 188–9 fishbone diagrams 463, 464 fit goodness of 407–10 line of best 221–8 Five whys method 462 fixed costs break-even point 190–7 in economies of scale 194–5 fixed order quantity 484, 494 float 515 forecasting 249–80 causal 225–8, 251 exponential smoothing 265–8 judgemental 251, 252–5 linear regression 221–8 methods 250–1, 275–7 moving averages 260–4, 271 projective 255–69 seasonality and trend 270–7 sensitivity 261, 267 simple averages 259–60 smoothing constant 265 time horizon 250–1 time series 255–9 formulation, linear programming 284–90 fractions 22–5 freedom, degrees of in Chi-squared 407–8 in t-distribution 385–7 frequency distributions 108–10, 336–8 cumulative 110 definition 108–10 measures of mean 139–40 mean absolute deviation 149–51 median 141–2 mode 142–4 skewness 156–7 standard deviation 152 variance 152 percentage 110 relative 336 frequency tables 106, 107 Gantt chart 518, 519 Gaussian distribution see Normal distribution gearing 189 goodness of fit test 407–10 gradient, straight line 56–7 graphs Cartesian co-ordinates 50–8, 111–14 drawing 50–72 exponential 64–5 formats 111–14 gradient 56–7 for linear programmes 290–6 polynomials 62–3 quadratic equations 59–61, 62 simultaneous equations 66–8 straight line 54–8 grouped data mean 139–40 mean absolute deviation 150 median 142 mode 144 standard deviation 152 variance 152 histograms 124–6 historical analogy 253–4 horizon, forecasting 250–1 hypothesis testing 392–419 aim 392–5 alternative hypothesis 393 association 412–14 Chi-squared test 407–10 differences in means 403–4 errors 394–5 goodness of fit 407–10 method 397–8 non-parametric tests 407 null hypothesis 393, 394 one-sided 398–401 paired tests 404–6 parametric tests 407 significance level 396–401 small samples 401–2 ideas in practice Argentia Life Assurance 290 AstraZeneca 189 automatic testing systems 406 BG Group 10 Bird Flu 376–7 Canada Revenue Agency 44 Channel Tunnel, The 506 CIS personal pensions 317 597 www.downloadslide.com 598 Index ideas in practice (continued ) Cosmetic advertisements 86 decisions involving uncertainty 365 El Asiento Rojolo 488 Emjit Chandrasaika 62 ExcelEst Education 277–8 Finding secondary data 84 forecasting oil prices 254–5 Goolongon Smelting 304 Hotel costing 243–4 Hughes, T.D., Ltd 26 Humbolt Farm Products 411–12 I’m no good at maths 14 Konrad Schimmer 65–6 La Milla Ferensa 175–6 Loch Moraigh Distillery 525–6 Long Barrow Farm 227–8 Mareco 95 Mattel Inc 458 medical testing 323 Meecham Financial Services 539 Melchior Trust ‘E’ 205 Microsoft Excel’s Solver 301–3 Misleading graphs 69–70 Mohan Dass and Partners 168 New York Containers 465 Opinion polls 382 Paco Menendes 432 Pengelly’s Restaurant 462–3 PhD research 99 politics and hypotheses 395 Prinseptia 158 renewable energy statistics 372 reports of findings 415 Retail Price index 176–7 retirement annuity 211 Richmond, Parkes and Wright 240 RPF Globa SaskPower 269 SAT reasoning test 122–3 SenGen Instrumental 548–50 Shingatsu Industries 352 software for drawing diagrams 129 stock holdings at Schultz-Heimleich 483 Stroh Brewery Company 473 Survey into use of quantitative methods 81 Symonds Logistics, H.J 433–4 Taco Bell 543–4 Taranangama Village Health Centre 146 Tax on house purchase 155 UK cereal production 110–11 US Coast Guard 331 Vancouver Electrical Factors 497–8 yield management in airlines 446 independent demand 481–2 independent events 317–18 independent variable 51, 111, 221 index number 163–78 aggregate 171–3 base period 164 base period weighting 173 calculations with 165–7 changing base period 169–71 current weighted 173–4 definition 164–5 mean price relative 171–2 weighted 172–6 indices see index inequalities 31–2 infeasible solution 304 information 77–81 integers 22 intercept 56–7 interest 197–200 annual percentage rate 200 compound 198–9 simple 198 internal failure costs 456 internal rate of return (IRR) 203–4 interquartile range 147–8 interval estimate 377 Inventory Forecasting System (DFS) 525 interviews personal 93 telephone 93 inventory management see stock control investment 198–200 Ishikawa diagrams 463 judgemental forecast 251, 252–5 labour productivity 187 Laplace decision criterion 428 Laspeyres index 173 lead time 487–8 line graph 50 line of best fit 221–8 linear programming 283–310 computer solutions 299–304 constraints 285–7 decision variables 287 definition 284 formulation 284–90 graphical solutions 290–6 non-negativity constraint 286 objective function 286–7 sensitivity analysis 284, 296–304 solving real problems 299–304 www.downloadslide.com Index linear regression 216–44 errors 217–18 for forecasting 221–8, 271 line of best fit 221–8 measuring relationships 216–20 multiple 235–9 noise 218–20 non-linear data 240–3 strength of relationship 228–34 linear relationship 55, 221–8 loans 209–10 location of data see mean logarithms 42–4 long term forecast 250 longitudinal survey 94 Lorenz curve 127–8 loss function 460 lot tolerance percent defective (LTPD) 467–8 MAD see mean absolute deviation marginal cost 196–7 marginal values 196–7 market survey 253 mean arithmetic mean 137–40 choice of measure 145 median 141–2 mode 142–4 of binomial distribution 344 of grouped data 139–40 of Normal distribution 354–7 of Poisson distribution 349 sampling distribution of 372–7 weighted 139 mean absolute deviation 149–51 of grouped data 150 mean absolute error 220, 258 mean deviation 149–50 mean error 219, 257–8 mean price relative index 171–2 mean squared deviation 151–4 mean squared error 220, 258 measures of change 163–8 of data 134–6 location 135–6, 136–45 spread 135–6, 146–54 of error 217–18 of noise 218–20 of performance 185–9 of relationship 228–34 median 141–2 for grouped data 142 mode 142–4 grouped data 144 model 7–8 model building 7–8 mortgages 208–10 most likely duration 521 moving average 260–4, 271 multicollinearity 237 multiple (linear) regression 235–9 multiplicative model 270 mutually exclusive events 319–22 natural logarithms 43 negative exponential distribution 534 net present value 201–3 internal rate of return 203–4 network analysis see project network analysis node in decision trees 440 in networks 506 in probability trees 328–30 noise in regression 218–20 in time series 255–6 nominal data 82 non-critical activities 517, 520 non-linear regression 240–3 non-linear relationship 58 non-negativity constraint 286 non-parametric tests Chi-squared 407–10 definition 407 non-response to questionnaires 96–8 Normal distribution 353–65 definition 353–4 shape 353–4 tables 590 use 357–65 notation, scientific 41–2 null hypothesis 393, 394 numbers arithmetic 20–1 changing to letters 27–9 index numbers 163–78 management and 5–6 working with 3–6, 20–6 numerator 22 objective function 286–7 changes in 298–9 observation for data collection 92 ogive 126–7, 142 599 www.downloadslide.com 600 Index one-sided confidence intervals 382–4 hypothesis test 398–401 operating characteristics 535–6 curve (OC curve) 468 operations optimal solution to linear programme 292–6 optimistic duration 521 ordinal data 82 origin 52 p-chart 470 Paasche index 174 panel consensus 252, 253 panel survey 94 parametric tests 407 Pareto analysis 498 Pareto chart 462, 463 partial productivity 187 payoff matrix 426 payoff table 426 Pearson coefficient of correlation 231–3 coefficient of skewness 156 percentage 24–5 percentage frequency distribution 110 percentage points 166 percentile 149 performance ratio 186–7 periodic review 484, 494–7 permutations 338–41 personal insight 252–3 personal interview 93 pessimistic duration 521 pictograms 121–2 pie charts 115–16 planning with linear programming 283–306 projects 504–26 point estimate 377 Poisson distribution 347–52 approximation to binomial 347–8 definition 347–8 for queues 534 shape 349–50 tables 586–9 polynomials 62–3 population definition 85, 371 estimating proportions 381, 403 positive quadrant 52 postal survey 93–4 powers 36–44 exponential function 42–4 logarithms 42–4 negative and fractional 39–40 scientific notation 41–2 present value of money 201–7 presentation of data 103–6 prevention costs 455 price-earnings ratio 189 price relative 171–2 primary data 83–4 probability Bayes’ theorem 324–8 calculations with 317–22 conditional 323–31 definitions 314–16 distributions 336–69 independent events 317–18 mutually exclusive events 319–22 tree 328–30 probability distributions 336–69 binomial 341–6, 581–5 Chi-squared 407–10 definition 336 empirical 337 negative exponential 534 Normal 353–65, 590 Poisson 347–52, 586–9 t 385–7, 591 problem map 424–6 problem-solving 7–11 model building 7–8 stages in 8–10 process control 464, 470–3 producer’s risk 467 product variability 459–61 productivity 187 profit 188 profit margin 188 project 505 project evaluation and review technique (PERT) 521–4 project network analysis 506–10 activity 506–7 critical path 514–16 definition 506 drawing networks 508–10 float 515 Gantt chart 518, 519 project timing 511–20 project planning 505–6 critical activities 514–16 resource levelling 518–20 projective forecast 251, 255–69 www.downloadslide.com Index exponential smoothing 265–8 moving averages 260–4, 271 seasonality and trend 269–77 simple averages 259–60 time series 255–9 quadratic equations 58–61 graphs 59–61 qualitative methods quality costs 455–7 definition 453 quality control 459–61 acceptance sampling 464, 465–9 definition 460 process control 470–3 product variability 459–61 tools for 461–4 quality gurus 458 quality management 454–5 quality measurement 452–8 quality revolution 455 quantitative methods 4, quartile 147–9 quartile deviation 147–8 queues 531–54 definition 532 features 531–3 Monte Carlo simulation 544–6 multi-server 538 operating characteristics 535–6 simulation 540–50 single server 533–8 questionnaire 92–3 design 95–6 non-responses 96–8 quota sample 90 random events 347–8 random node 440 random numbers 87–8 random sample 87–8 range 147–9 rank correlation 233–4 ratios for finance 188–9 rectangular axes 51–4 reducing-balance depreciation 206–7 reduction of data 103–6 regression see linear regression relative frequency distribution 336 reorder level constant demand 487–8 variable demand 491–4 residual factor 270 resources levelling 518–20 linear programming 297–8 Retail Price Index 176–7 return on equity 189 return on total assets 188 decision making with 432–9 expected value 432–3 updating probabilities 434–6 utility 437–8 roots of numbers 36–44 of quadratic equations 61 rounding 25–6 routine sampling 464 rule of sixths 521 safety stock 492–4, 496–7 sample data collection 85–91 definition 85, 371 purpose 371 random 87–8 small 385–7 types 86–91 sampling 370–91 acceptance 464, 465–9 by attribute 466 confidence interval 377–82 data collection 85–91 distribution of sample mean 372–7 frame 85 for population proportions 381 for quality control 459–65 one-sided interval 382–4 process control 470–3 purpose 370–1 questionnaire 92–3 random 87–8 t-distribution 385–7 by variable 465 Savage decision criterion 429–30 scatter diagram 111–12 scheduling combinations and permutations 338–41 number of sequences 338–9 projects 504–26 scientific notation 41–2 seasonal factor 270 seasonal index 274–5 seasonal series 255 secondary data 83–4 601 www.downloadslide.com 602 Index semi-interquartile range 147–8 sensitivity analysis (in LP) 284, 296–304 changes in objective function 298–9 changes in resources 297–8 sensitivity of forecasts 261 sequencing 338–9 sequential decisions 439–45 service level 491–4, 496 shadow price 297–8 significance level 396–401 significant figures 25 simple aggregate index 172 simple average forecast 259–60 simulation approach 540–50 definition 540 Monte Carlo 544–6 simultaneous equations 32–6 finding variables 35–6 graphs 66–8 solving 33–4 single-server queue 533–8 sinking funds 208–10 skewness 156–7 slack 515 software 12–14 solving equations 29–32 linear programmes 290–6 problems 7–10 quadratic equations 58–61 simultaneous equations 33–5 Spearman’s coefficient 233–4 spread of data 135–6, 146–54 mean absolute deviation 149–51 mean deviation 149–50 mean squared deviation 151–4 quartile deviation 147–8 range 147–9 semi-interquartile range 147–8 standard deviation 151–4 variance 151–4 spreadsheets 13–14, 54 square root 39 standard deviation 151–4 correcting 380–1 grouped data 152 of binomial distribution 344 of Normal distribution 354–7 of Poisson distribution 349 sample 379–80 standard error 375 statistical inference 371 statistical tables 581–93 statistics probability 313–69 probability distributions 336–69 sampling 370–419 testing 392–419 stochastic problems 313 stock classification 480–1 definition 480 types 480–1 stock control 479–503 ABC analysis 498–9 approaches 481–2 background 480–3 costs 482–3 economic order quantity 484–8 periodic review 494–7 for production 489–90 reorder level 487–8 service level 491–4 variable demand 491–4 straight line depreciation 205–6 straight line graphs 54–8 stratified sample 89–90 strict uncertainty 428 survey e-mail 94 longitudinal 94 panel 94 postal 93–4 questionnaires 92–3 symbolic models systematic sample 89 t-distribution 385–7, 591 tables of data 106–11 binomial distribution 581–5 Chi-squared distribution 592–3 frequency tables 106, 107 Normal distribution 590 Poisson 586–9 t-distribution 591 target stock level 495–7 telephone interview 93 terminal node 440 testing hypotheses see hypothesis testing time series 255–9 total float 515, 520 Total Quality Management (TQM) 455, 459–61 tree decision 439–45 probability 328–30 www.downloadslide.com Index trend 255, 270 finding 271–3 turning points 59 Type I error 394, 395, 467 Type II error 394, 395, 467 unbound solution 304 uncertainty decision making with 427–31 measuring 313–17 risk 432–9 utilisation 186–7 utility 437–8 value of data 80–1 of money over time 201–7 variable definition 28 in linear regression 218–20 variable cost 190–7 variance 151–4 grouped data 152 of binomial distribution 344 of Normal distribution 354–7 of Poisson distribution 349 variation, coefficient of 155 Venn diagrams 320–1 Wald decision criterion 428–9 weighted index 172–6 weighted mean 139 yield 189 603 www.downloadslide.com .. .Quantitative Methods for Business Visit the Quantitative Methods for Business, Fifth Edition companion website at www.pearsoned.co.uk /waters to find valuable student... for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Waters, C D J (C Donald J.), 1949– Quantitative methods for business / Donald Waters — 5th. .. book on quantitative methods for business and management The book: n n n n n n n n n is an introductory text that assumes no previous knowledge of business, management or quantitative methods