Business Mathematics and Statistics

632 Pages·2019·50.21 MB·English

by  Ram Ghosh

Business Mathematics
and Statistics
(Algebra, Geometry
and Business Statistics)
Ram Krishna Ghosh
Suranjan Saha
BUSINESS
MATHEMATICS AND STATISTICS
[For BCom First Year General & Honours Students]
"This page is Intentionally Left Blank"
Written according to the BCo m, First Year New Syllabus ofC alcutta University.
ALro covers the syllabi of Vidyasagar, North Bengal and Burdwan Universities.
Useful to the students ofM BA, CA, ICWAI and other professional courses as well.
BUSINESS
MATHEMATICS AND STATISTICS
[For BCom First Year General and Honours Students
and Other Professional Examinations.]
Ram Krishna Ghosh
Formerly, Head, Department of Mathematics, St. Xavier's College, Kolkata
Sometime Senior Lecrurer in Mathematics, University of Cape Coast, Ghana
Sometime Pan-time Lecturer in Mathematics, University of Kalyani, Kalyani, WB
Formerly, President, Institute of Modern Management, Kolkata
and Director, Academy of Civil Services, Kolkata
Suranjan Saha
Formerly, Head, Department of Mathematics & Statistics,
Heramba Chandra College [City College, South Kolkata]
Formerly, Pan-time Lecturer in Mathematics & Statistics,
Sivanath Sastri College and Shri Shikshayatan College, Kolkata
Sometime Part-rime Honorary Lecturer in
Business Mathematics & Statistics, ICWAI
Strictly as per the New Syllabus-effective from 20.15 onwards
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BUSINESS MATHEMATICS AND STATISTICS • Ram Krishna Ghosh, Suranjan Saha
© Copyright reserved by the Authors
Publication, Distribution, and Promotion Rights reserved by the Publisher
All rights reserved. No part of the text in general, and the figures, diagrams, page layout,
and cover design in particular, may be reproduced or transmitted in any form or by any
means-electronic, mechanical, photocopying, recording, or by any information storage
and retrieval system-without the prior written permission of the Publisher
First Published: 1979
Thirteenth Edition: 2010
Reprinted: 2011, 2012, 2013, 2014
Fourteenth Revised Edition (New Syllabus): 2015
Repri11ted: 2016
PUBLISHER
Central Educational Enterprises (P) Ltd
54B Patuatola Lane, Kolkata 700 009
TYPESETTER
New Central Book Agency (P) Ltd
8/1 Chintamoni Das Lane, Kolkata 700 009
PRINTER
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COVER DESIGNER
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TECHNICAL EDITOR
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PROJECT TEAM
Abhijit Sen and Pradip Biswas
ISBN; 978 81 7381 975 9
... Price Z 385.00
"This page is Intentionally Left Blank"
CONTENTS
Preface to the Thirteenth Edition vii
Preface to the Eleventh Edition vii
Preface to the First Edition viii
Revised Syllabus "ix-x
Important Formulae and Results xi-xxi
BUSINESS MATHEMATICS AND STATISTICS
MODULE I (50 Marks)
ALGEBRA
Unit
1. Permutations 5-25
2. Combinations 26-49
3. Logarithms 5()..69
4. Elements of Set Theory 70-106
5. Binomial Theorem ... 107-126
6. Compound Interest and Compounding 127-142
7. Annuities:. Sinking Fund ... 143-172
STATISTICS
8. Introduction: Definition of Statistics: Importance and Scope, Types, Sources and
Collection of Data 175-190
9. Summarization of Data: Classification and Tabulation; Frequency Distribution 191-219
10. Diagrammatic Representation of Statistical Data . .. 220-261
11. Measures of Central Tendency: Mean, Median and Mode .. . 262-317
12. Measures of Dispersion ... 318-350
MODULE II [50 Marks}
13. Moments, Measures of Skewness and Kurtosis ... 353-372
14. Correlation and Regression ... 373-412
15. Probability Theory ... 413-458
16. Interpolation ... 459-481
17. Index Numbers ... 482-543
18. Time Series Analysis ... 544-590
19. Measures of Association of Attributes ... 591-601
Appendix: Logarithms and Antilogarithms i-viii
Calcutta University B Com Examination Questions 1-
lvJ
"This page is Intentionally Left Blank"
Preface to the Thirteenth Edition
The present volume is a thoroughly revised thirteenth edition of our textbook Business
Mathematics and Statistics strictly conforming to the new syllabus prescribed by the University
of Calcutta effective from the Academic Session 2010-11. In this edition, a large number of
problems set in B.Com. General and Honours Examinations of Calcutta, Burdwan and North
Bengal Universities held during 2006-2009 have been solved in each chapter of the book. This
book is meant for all B.Com. first year Pass and Honours students.
Any suggestion/criticism from the readers will be gratefully received.
Kolkata R. K. Ghosh
15 August 2010 S. Saha
Preface to the Eleventh Edition
'The present volume is a thoroughly revised edition of our textbook Business Mathematics
and Statistics strictly according to the new (revised) syllabus prescribed by the University of
Calcutta to be effective from the academic session 2006-07.
Dne to the changes in the new syllabus some of the topics of the earlier edition (e.g.,
Partial Differentiation, Differentials: Total Differentials and their Applications, Theory of
Probability and Concept of Random Variable and Probability Distribution) had to be dropped.
According to the new syllabus, one new topic (e.g., Discounting) had to be inserted to Part II:
Mathe:µiatics of Finance. Also several typical problems from the current examination papers
have been added in each chapter of the book.
Any suggestion or criticism from our beloved students and their esteemed teachers will be
gratefully received.
Kolkata R. K. Ghosh
9 May 2006 S. Saha
[vii J
Preface to the First Edition
Nowadays the knowledge of MATHEMATICS AND STATISTICS is considered essential for
a scientific approach to business problems and also for profitable business decisions. The
importance of Mathematics is found to be reflected in the revised curriculum of the commerce
course in different universities and professional institutes. The present treatise is intended as
a textbook of Business Mathematics and Statistics for all the aforesaid courses. In particular,
the syllabi prescribed by the University of Calcutta for the two-year B.Com. Course under the
10 + 2 + 2 system have been followed very closely.
In preparing the text we have taken into consideration the fact that many students who
take up a business career have had a far less thorough grounding in mathematics than those
entering into pure science courses. The book, therefore, has been written in a language that
is easy to follow; theory and applications 'run side by side; illustrated diagrams are plenty.
An adequate number of carefully chosen examples are worked out and hints for solving harder
problems are given at the end of each exercise. In every exercise, gradation of problems has
been made with utmost care. In order to give our readers an idea of the standard expected by
different examining bodies we have incorporated a number of questions set previously for the
B.Com., Cost and Chartered Accountancy Examinations.
The book is divided into three parts-Algebra, Elements of Co-ordinate Geometry
and Business Statistics, covering the entire syllabus of the B.Com. Pass Courses of different
universities of West Bengal and other States of the country. In each part, new and difficult
concepts have been dealt with the greatest possible clarity, taking illustrations from real-life
situations. In -short, every attempt has been made to create interest in the subject among the
young learners. How far the authors have been successful in their endeavour shall be judged
by the readers themselves.
The authors deeply regret the inconvenience caused to the students for the unavoidable
delay in the publication of the book. The major constraint was the uncertain working hours of
the press due to load-shedding. The authors do not believe that the book is free from printing
mistakes though all care has been taken to avoid them. Suggestions for further improvement
of the book and correction of printing errors, if any, will be most gratefully received.
The authors wish to record their deep obligation and gratitude to the late Professor Ajit
Kumar Basu with whom the first author jointly wrote the book Commercial Mathematics
(Ghosh and Basu). It will not be surprising to find some influence of that boo1<. on the present
treatise.
We finally record our great appreciation of the work done by the staff who had to work
under heavy constraints in bringing out the present volume.
Calcutta R. K. Ghosh
Rathajatra, 26 June 1979 S. Saha
[viii]