Business Mathematics and Statistics

747 Pages·2012·38.606 MB·English

by  N Das, Dr. J K Das

Business Mathematics
and Statistics
ABOUT THE AUTHORS
(Late) N G Das was Professor-in-charge of the Department of Statistics, St. Xavier's
College, Kolkata. He also served as a Lecturer in Goenka College of Commerce and
Business Administration, Kolkata.
J K Das is currently Associate Professor in the Department of
Commerce, University of Calcutta. He has been teaching business
statistics, business mathematics, operations research, research
methodology and marketing research at postgraduate level for over
two decades. A PhD in Statistics from University of Calcutta,
Dr Das has also supervised a number of PhD dissertations in
commerce as well as management subjects. He has to his credit a
significant number of research papers published in journals of
national and international repute. He has also authored in the past, books on business
statistics for undergraduate and postgraduate students.
Dr Das is member of Board of Studies as well as Visiting Professor in different institutes
and universities and has designed syllabi for a number of courses. He has been
associated with numerous selection boards as an expert in quantitative techniques
and has also undertaken a number of consultancy and research projects entailing the
use of applied statistics.
Business Mathematics
and Statistics
(Late) N G DAS
Formerly, Professor-in-charge
Department of Statistics
St. Xavier’s College, Kolkata
and
Lecturer, Goenka College of Commerce and
Business Administration, Kolkata
J K DAS
Associate Professor
Department of Commerce
University of Calcutta, Kolkata
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Dedicated to
Revered
Shri Swayambhu Prasad Roy
and
Smt Chhaya Roy
–J K Das

PREFACE
A sound knowledge of mathematical and statistical techniques is very much essential
to study the modern problems in business. As a result, business mathematics and
statistics becomes a mandatory subject for the students of commerce and management
streams.
Over the last two decades, while teaching statistics and mathematics to commerce
and management students, I felt the need for a compact book on the subject which
could fulfil the requirements of undergraduate students. Thus, the primary objective
in writing this book is to explain the concepts of business mathematics and statistics
in a simple, lucid and logical way. For easy readability and understanding, complicated
derivations have been avoided as far as possible. Numerous business-oriented examples
have been presented and solved throughout the text. Unsolved problems with hints
and answers have been added in each chapter to strengthen the conceptual as well as
practical knowledge of students.
This book is a humble attempt to provide the students with a comprehensive and
balanced coverage of theory and problems of mathematical and statistical techniques
applicable to the world of commerce and management. It enables the students to
understand the basic concepts and apply the useful formulae and results directly to
the business problems. It is aimed at meeting the requirements of undergraduate
students of commerce and management streams. It has been designed as per the new
syllabus of BCom Part I (Honours and General) of the University of Calcutta. However,
it will be equally useful for BCom, BBA and similar other undergraduate courses of
different universities in India.
Each chapter of the book first discusses basic concepts and then moves on to delve
into the advanced concepts. The text includes real-life problems, both solved and
unsolved, applying different mathematical and statistical techniques. A large number
of illustrative examples have been solved to explain the concepts. Unsolved problems
included in each chapter will enable the students to assess their understanding of the
concepts. Solutions for last five years’ question papers from University of Calcutta
(whenever the respective chapter was included in the syllabus) relevant to the present
syllabus have been provided for ready reference. This will help the students to prepare
themselves for this course without any additional guidance. Some advanced examples
are given for the benefit of highly ambitious students. Since most of the students of
commerce and management lack a formal mathematical background, some useful
mathematical and statistical formulae and results relating to different chapters are
provided in the begining of the book. I hope the students will find the book highly
informative and useful in its present form.
I wish to place on record my deep respect and gratitude to the late Prof. N G Das.
A number of chapters in this book have been derived from his works. I am extremely
grateful to the staff of the editorial and production departments of Tata McGraw-Hill,
in particular to Ms Piyali Ganguly, Mr Santanu Basu, Mr Hemant Kumar Jha, MrVijay
Sarathi, and Mr Manohar Lal for their cordial co-operation and encouragement.
viii Preface
I appreciate the sacrifices and the unflagging support of my mother, wife and
daughters while I was engaged in preparing the manuscript. I am thankful to my
students Shabana, Tina, Sharad, Biman and Sandip, who assisted me during the period
when the book was under preparation.
I request the readers to send their valuable comments and suggestions for further
improvement, so that these can be taken care of in future editions.
J K DAS
[email protected]
SYLLABUS
UNIVERSITY OF CALCUTTA
Common Paper for B.Com. Honours and General
BUSINESS MATHEMATICS AND STATISTICS
Module I [50 marks]
Unit
1. Introduction – Definition of Statistics; Importance and scope of Mathematics
and Statistics in business decisions; Limitations. [2 lectures / 2 Marks]
2. Permutations – Definition, Factorial notation; Theorems on permutation,
permutations with repetitions; Restricted permutations. [4 lectures / 4 Marks]
3. Combinations – Definition; Theorems on combination; Basic identities;
Restricted combinations. [4 lectures / 4 Marks]
4. Set Theory – Definition of Set; Presentation of Sets; Different types of Sets-
Null Set, Finite and Infinite Sets, Universal Set, Subset, Power Set etc.; Set
operations; Laws of algebra of Sets. [6 lectures / 6 Marks]
5. Logarithm – Definition, Base and index of logarithm, general properties of
logarithm, Common problems. [4 lectures / 4 Marks]
6. Binomial Theorem – Statement of the theorem for positive integral index,
General term, Middle term, Equidistant terms, Simple properties of binomial
coefficient. [4 lectures / 4 Marks]
7. Compound Interest and Annuities – Different types of interest rates; Concept
of Present value and amount of sum; Types of annuities; Present value and
amount of an annuity; including the case of continuous compounding; Valuation
of simple loans and debentures; Problems relating to sinking funds.
[8 lectures / 8 Marks]
8. Collection, Classification and Presentation of Statistical Data – Primary
and Secondary data; Methods of data collection; Tabulation of data; Graphs
and charts; Frequency distributions; Diagrammatic presentation of frequency
distributions. [8 lectures / 8 Marks]
9. Measures of Central Tendency – Common measures of central tendency –
mean, median and mode; Partition values – quartiles, deciles, percentiles.
[6 lectures / 6 Marks]
10. Measures of Dispersion – Common measures of dispersion – range, quartile
x Syllabus
deviation, mean deviation and standard deviation; Measures of relative
dispersion. [4 lectures / 4 Marks]
BUSINESS MATHEMATICS AND STATISTICS
Module II: [50 marks]
Unit
11. Moments, Skewness and Kurtosis – Different types of moments and their
relationships; Meaning of skewness and kurtosis; Different measures of
Skewness and Kurtosis. [6 lectures / 6 Marks]
12. Correlation and Regression – Scatter diagram; Simple correlation coefficient;
Simple regression lines; Spearman’s rank correlation ; Measures of association
of attributes. [8 lectures / 8 Marks]
13. Probability Theory – Meaning of probability; Different definitions of
probability; Conditional probability; Compound probability; Independent events;
(excluding Bayes’ Theorem). [10 lectures / 10 Marks]
14. Interpolation – Finite differences; Newton’s forward and backward inter-
polation formula; Lagrange’s interpolation formula. [6 lectures / 6 Marks]
15. Index Numbers – Means and types of index numbers ; Problems in construction
of index numbers; Methods of construction of price and quantity indices; Tests
of adequacy; errors in index numbers; Chain-base index numbers; Base shifting,
splicing, deflating; Consumer price index and its uses.
[10 lectures / 10 Marks]
16. Time Series Analysis – Causes of variation in time series data; Components of
time series ; Additive and multiplicative models; Determination of trend by
semi average, moving average and least squares(linear, second degree and
exponential) methods; Computation of seasonal indices by simple average, ratio-
to-moving average, ratio-to trend and link relative methods; Simple forecasting
through time series data. [10 lectures / 10 Marks]