,Cambridge
International AS and A Level Mathematics
Statistics
Sophie Goldie
Series Editor: Roger Porkess
,Questions from the Cambridge International Examinations AS and A Level Mathematics papers
are reproduced by permission of University of Cambridge International Examinations.
Questions from the MEI AS and A Level Mathematics papers are reproduced by permission of OCR.
We are grateful to the following companies, institutions and individuals who have given permission
to reproduce photographs in this book.
Photo credits: page 3 © Artur Shevel / Fotolia; page 77 © Luminis / Fotolia; page 105 © Ivan Kuzmin / Alamy; page 123
© S. Ferguson; page 134 © Peter Küng / Fotolia; page 141 © Mathematics in Education and Industry; p.192 © Claudia
Paulussen / Fotolia.com; page 202 © Ingram Publishing Limited; page 210 © Peter Titmuss / Alamy; page 216 © Monkey
Business / Fotolia; page 233 © StockHouse / Fotolia; page 236 © Ingram Publishing Limited / Ingram Image Library
500-Animals; page 256 © Kevin Peterson / Photodisc / Getty Images; page 277 © Charlie Edwards / Getty Images;
page 285 © Stuart Miles / Fotolia.com
All designated trademarks and brands are protected by their respective trademarks.
Every effort has been made to trace and acknowledge ownership of copyright. The publishers will be
glad to make suitable arrangements with any copyright holders whom it has not been possible to contact.
Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and
made from wood grown in sustainable forests. The logging and manufacturing processes are
expected to conform to the environmental regulations of the country of origin.
Orders: please contact Bookpoint Ltd, 130 Milton Park, Abingdon, Oxon OX14 4SB.
Telephone: (44) 01235 827720. Fax: (44) 01235 400454. Lines are open 9.00–5.00, Monday
to Saturday, with a 24-hour message answering service. Visit our website at www.hoddereducation.co.uk
Much of the material in this book was published originally as part of the MEI Structured
Mathematics series. It has been carefully adapted for the Cambridge International AS and A Level
Mathematics syllabus.
The original MEI author team for Statistics comprised Michael Davies, Ray Dunnett, Anthony Eccles,
Bob Francis, Bill Gibson, Gerald Goddall, Alan Graham, Nigel Green and Roger Porkess.
Copyright in this format © Roger Porkess and Sophie Goldie, 2012
First published in 2012 by
Hodder Education, an Hachette UK company,
338 Euston Road
London NW1 3BH
Impression number 54321
Year 2016 2015 2014 2013 2012
All rights reserved. Apart from any use permitted under UK copyright law, no part of this
publication may be reproduced or transmitted in any form or by any means, electronic or
mechanical, including photocopying and recording, or held within any information storage
and retrieval system, without permission in writing from the publisher or under licence from
the Copyright Licensing Agency Limited. Further details of such licences (for reprographic
reproduction) may be obtained from the Copyright Licensing Agency Limited, Saffron
House, 6–10 Kirby Street, London EC1N 8TS.
Cover photo © Kaz Chiba/Photodisc/Getty Images/Natural Patterns BS13
Illustrations by Pantek Media, Maidstone, Kent
Typeset in 10.5pt Minion by Pantek Media, Maidstone, Kent
Printed in Dubai
A catalogue record for this title is available from the British Library
ISBN 978 1444 14650 9
, Contents
Key to symbols in this book vi
Introduction vii
The Cambridge International AS and A Level Mathematics syllabus viii
S1 Statistics 1 1
Chapter 1 Exploring data 2
Looking at the data 4
Stem-and-leaf diagrams 7
Categorical or qualitative data 13
Numerical or quantitative data 13
Measures of central tendency 14
Frequency distributions 19
Grouped data 24
Measures of spread (variation) 34
Working with an assumed mean 45
Chapter 2 Representing and interpreting data 52
Histograms 53
Measures of central tendency and of spread using quartiles 62
Cumulative frequency curves 65
Chapter 3 Probability 77
Measuring probability 78
Estimating probability 79
Expectation 81
The probability of either one event or another 82
Independent and dependent events 87
Conditional probability 94
Chapter 4 Discrete random variables 105
Discrete random variables 106
Expectation and variance 114
iii
International AS and A Level Mathematics
Statistics
Sophie Goldie
Series Editor: Roger Porkess
,Questions from the Cambridge International Examinations AS and A Level Mathematics papers
are reproduced by permission of University of Cambridge International Examinations.
Questions from the MEI AS and A Level Mathematics papers are reproduced by permission of OCR.
We are grateful to the following companies, institutions and individuals who have given permission
to reproduce photographs in this book.
Photo credits: page 3 © Artur Shevel / Fotolia; page 77 © Luminis / Fotolia; page 105 © Ivan Kuzmin / Alamy; page 123
© S. Ferguson; page 134 © Peter Küng / Fotolia; page 141 © Mathematics in Education and Industry; p.192 © Claudia
Paulussen / Fotolia.com; page 202 © Ingram Publishing Limited; page 210 © Peter Titmuss / Alamy; page 216 © Monkey
Business / Fotolia; page 233 © StockHouse / Fotolia; page 236 © Ingram Publishing Limited / Ingram Image Library
500-Animals; page 256 © Kevin Peterson / Photodisc / Getty Images; page 277 © Charlie Edwards / Getty Images;
page 285 © Stuart Miles / Fotolia.com
All designated trademarks and brands are protected by their respective trademarks.
Every effort has been made to trace and acknowledge ownership of copyright. The publishers will be
glad to make suitable arrangements with any copyright holders whom it has not been possible to contact.
Hachette UK’s policy is to use papers that are natural, renewable and recyclable products and
made from wood grown in sustainable forests. The logging and manufacturing processes are
expected to conform to the environmental regulations of the country of origin.
Orders: please contact Bookpoint Ltd, 130 Milton Park, Abingdon, Oxon OX14 4SB.
Telephone: (44) 01235 827720. Fax: (44) 01235 400454. Lines are open 9.00–5.00, Monday
to Saturday, with a 24-hour message answering service. Visit our website at www.hoddereducation.co.uk
Much of the material in this book was published originally as part of the MEI Structured
Mathematics series. It has been carefully adapted for the Cambridge International AS and A Level
Mathematics syllabus.
The original MEI author team for Statistics comprised Michael Davies, Ray Dunnett, Anthony Eccles,
Bob Francis, Bill Gibson, Gerald Goddall, Alan Graham, Nigel Green and Roger Porkess.
Copyright in this format © Roger Porkess and Sophie Goldie, 2012
First published in 2012 by
Hodder Education, an Hachette UK company,
338 Euston Road
London NW1 3BH
Impression number 54321
Year 2016 2015 2014 2013 2012
All rights reserved. Apart from any use permitted under UK copyright law, no part of this
publication may be reproduced or transmitted in any form or by any means, electronic or
mechanical, including photocopying and recording, or held within any information storage
and retrieval system, without permission in writing from the publisher or under licence from
the Copyright Licensing Agency Limited. Further details of such licences (for reprographic
reproduction) may be obtained from the Copyright Licensing Agency Limited, Saffron
House, 6–10 Kirby Street, London EC1N 8TS.
Cover photo © Kaz Chiba/Photodisc/Getty Images/Natural Patterns BS13
Illustrations by Pantek Media, Maidstone, Kent
Typeset in 10.5pt Minion by Pantek Media, Maidstone, Kent
Printed in Dubai
A catalogue record for this title is available from the British Library
ISBN 978 1444 14650 9
, Contents
Key to symbols in this book vi
Introduction vii
The Cambridge International AS and A Level Mathematics syllabus viii
S1 Statistics 1 1
Chapter 1 Exploring data 2
Looking at the data 4
Stem-and-leaf diagrams 7
Categorical or qualitative data 13
Numerical or quantitative data 13
Measures of central tendency 14
Frequency distributions 19
Grouped data 24
Measures of spread (variation) 34
Working with an assumed mean 45
Chapter 2 Representing and interpreting data 52
Histograms 53
Measures of central tendency and of spread using quartiles 62
Cumulative frequency curves 65
Chapter 3 Probability 77
Measuring probability 78
Estimating probability 79
Expectation 81
The probability of either one event or another 82
Independent and dependent events 87
Conditional probability 94
Chapter 4 Discrete random variables 105
Discrete random variables 106
Expectation and variance 114
iii
