ATSWA Study Pack - Quantitative Analysis - The Institute of

386 Pages·2012·2.82 MB·English

NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
QUANTITATIVE ANALYSIS

FOR

ACCOUNTING TECHNICIANS SCHEME OF WEST AFRICA
(ATSWA)
STUDY PACK

i
NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.

Copy (c) 2009 by Association of Accountancy bodies in West Africa (ABWA). No rights
reserved. No part of this publication may be reproduced or distributed in any form or by any
means, or stored in a database or retrieval system, without the prior written consent of the
copyright owner. Including, but not limited to, in any network or other electronic storage or
transaction or broadcast for distance learning.

Published by
ABWA PUBLISHERS
Akintola Williams House
Plot 2048, Michael Okpara Street
Off Olusegun Obasanjo Way
Zone 7, P. O. Box 7726
Wuse District, Abuja, FCT
Nigeria.

DISCLAIMER
The book is published by ABWA, however, the views are entirely that of the writers.

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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.

CONTENTS
Preface ............................................................................................................................. v
Forward .............................................................................................................................. vii
Acknowledgment ...............................................................................................................viii

CHAPTER ONE - Statistics, Data Collection and Summary................................................3
1.0 Learning Objectives .............................................................................................................3
1.1 Introduction .........................................................................................................................3
1.2 Type of Data.........................................................................................................................3
1.3 Methods of Data collection ..................................................................................................4
1.4 Presentation of Data.............................................................................................................6
1.5 Sampling Techniques .........................................................................................................14
1.6 Errors and Approximation ..................................................................................................20
1.7 Summary..............................................................................................................................23
1.8 Questions and Answers ........................................................................................................23

CHAPTER TWO – Measures of Locations ...........................................................................26
2.0 Learning Objectives ............................................................................................................26
2.1 Introduction ........................................................................................................................26
2.2 Mean ...................................................................................................................................26
2.3 Mode and median ...............................................................................................................34
2.4 Measures of Partition ...........................................................................................................43
2.5 Summary ............................................................................................................................46
2.6 Question and Answers..........................................................................................................46

CHAPTER THREE - Measures of Variations ..........................................................................49
3.0 Learning objectives ..............................................................................................................49
3.1 Introduction ........................................................................................................................49
3.2 Measures of Spread .............................................................................................................49
3.3 Coefficient of Variation and of Skewness ............................................................................57
3.4 Summary .............................................................................................................................59
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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
3.5 Questions and answers ........................................................................................................60

CHAPTER FOUR - Measure of Relationship and Regression ...............................................62
4.0 Learning Objectives ..............................................................................................................62
4.1 Introduction ..........................................................................................................................62
4.2 Types of Correlation ............................................................................................................63
4.3 Measures of Correlation .......................................................................................................63
4.5 Simple Regression Line ..........................................................................................................72
4.6 Coefficient of Determination ................................................................................................79
4.7 Summary .............................................................................................................................80
4.8 Question and Answer ..........................................................................................................80

CHAPTER FIVE – Time Series Analysis ..................................................................................83
5.0 Learning Objectives ......................................... ..................................................................83
5.1 Introduction ..........................................................................................................................83
5.2 Basic Components of a Time Series ....................................................................................84
5.3 Time Series Analysis ...........................................................................................................87
5.4 Estimation of Trend .............................................................................................................88
5.5 Estimation of Seasonal Variation .........................................................................................97
5.6 Summary ...............................................................................................................................101
5.7 Questions and Answers .....................................................................................................101

CHAPTER SIX – Index Numbers .........................................................................................105
6.0 Learning Objective ......................................... ....................................................................105
6.1 Introduction .......................................................................................................................105
6.2 Construction Methods of Price Index Numbers .................................................................107
6.3 Unweighted Index Numbers ..............................................................................................107
6.4 Weighted Index Numbers .....................................................................................................110
6.5 Construction of Quality Index Number ..............................................................................115
6.6 Summary ...........................................................................................................................115
6.7 Questions and Answers .......................................................................................................116
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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.

CHAPTER SEVEN Set Theory and probability.....................................................................119
7.0 Learning Objectives ......................................... ..................................................................119
7.1 Introduction ........................................................................................................................119
7.2 Concept of Probability theory ............................................................................................126
7.3 Addition of Law of Probability ..........................................................................................132
7.4 Conditional Probability and Independence ..........................................................................134
7.5 Multiplication Law of Probability .....................................................................................136
7.6 Mathematical Expectation ...................................................................................................137
7.7 Some Special Probability Distributions................................................................................139
7.8 Summary ...........................................................................................................................115
7.9 Questions and Answers ......................................................................................................116

CHAPTER EIGHT - Statistical Inference .............................................................................152
8.0 Learning Objectives ......................................... ..................................................................152
8.1 Introduction ........................................................................................................................152
8.2 Basic Concepts of Estimation ..............................................................................................152
8.3 Point Estimation of the Population Mean ..........................................................................154
8.4 Point Estimation of the population proportion ..................................................................156
8.5 Useful concepts in hypothesis Testing ..............................................................................157
8.6 Testing Hypothesis about a Population Parameters ...........................................................159
8.7 Testing Hypothesis about a Population Proportion ...........................................................163
8.8 Summary ...........................................................................................................................164
8.9 Questions and Answers .......................................................................................................164

CHAPTER NINE - Functions .......... ...................................................................................168
9.1 Definition of a Function ...................................................................................................168
9.2 Types of Function.............................................................................................................168
9.3 Equations .......................................................................................................................169
9.4 Inequalities and their Graphical Solutions ..........................................................................177
9.5 Application to Business, Economics and Management Problems ......................................190
9.6 Summary ..............................................................................................................................201
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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
9.7 Questions and Answers ....................................................................................................201
CHAPTER TEN - Mathematics of Finance....... ............................................................. ........204
10.1 Sequence and Series .......................................................................................................204
10.2 Simple Interest ................................................................................................................211
10.3 Compound Interest ...........................................................................................................212
10.4 Annuities .........................................................................................................................215
10.5 Summary .........................................................................................................................218
10.6 Questions and Answers ....................................................................................................219

CHAPTER TWELVE - Differential and Integral Calculus ..................................................242
12.1 Differentiation .................................................................................................................242
12.2 Basic rule for Differentiation ..........................................................................................243
12.3 Maximum and Minimum point; Marginal Functions; Elasticity..........................................246
12.4 Integration ........................................................................................................................253
12.5 Rules of Integration ...........................................................................................................254
12.6 Totals from Marginal .......................................................................................................256
12.7 Consumers‟ Surplus and Producers‟ Surplus...................................................................258
12.8 Summary .........................................................................................................................264
12.9 Questions and Answers ......................................................................................................264

CHAPTER THIRTEEN - Introduction to Operation Research .........................................268
13.1 Meaning and Nature of Operation Research ....................................................................268
13.2 Techniques of Operation Research .................................................................................270
13.3 Uses and Relevance of Operation Research in Business...................................................272
13.4 Limitation of Operation Research ...................................................................................273
13.5 Summary ........................................................................................................................273
13.6 Questions and Answers ..................................................................................................273

CHAPTER FOURTEEN - Introduction to Operations Research ........................................268
14.1 Introduction .....................................................................................................................268
13.2 Techniques of Operation Research ...................................................................................270
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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
13.3 Uses and Relevance of Operation Research in Business...................................................272
13.4 Limitation of Operation Research ....................................................................................273
13.5 Summary .........................................................................................................................273
13.6 Questions and Answers .....................................................................................................273

CHAPTER FOURTEEN – Linear Programming .................................................................275
14.1 Introduction ......................................................................................................................275
14.2 Concepts and Notations of Linear Programming ..............................................................275
14.3 Graphical Solution of Linear Programme Problems .........................................................276
14.4 Duality Problem ..................................................................................................................282
14.5 The Transportation Model ...............................................................................................285
14.6 Solving Transportation Problems.....................................................................................292
14.7 Summary ............................................................................................................................292
14.8 Questions and Answers ...................................................................................................292

CHAPTER FIFTEEN – Inventory Planning and Product Control.......................................297
15.1 Meaning and Functions of Inventory .............................................................................297
15.2 Inventory Cost ................................................................................................................298
15.3 Definition of Terminology ...............................................................................................299
15.4 General Inventory Models ...............................................................................................301
15.5 Basic Economic Order Quantity (EOQ) Model ................................................................303
15.6 Economic Order Quantity with Stockout ............................................................................307
15.7 Economic Order Quantity with bulk discounts ..................................................................307
15.8 Summary .........................................................................................................................309
15.9 Questions and Answers ...................................................................................................309

CHAPTER SIXTEEN – Network Analysis ..............................................................................312
16.1 Introduction ....................................................................................................................312
16.2 Construction/Drawing of a Network Diagram ................................................................314
16.3 Earliest Start Time (EST), Latest Start Time (LST) and Floats .........................................317
16.4 Summary ........................................................................................................................309
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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
16.5 Questions and Answer ......................................................................................................309
Exercises and Solutions ..........................................................................................................324
Bibliography ............................................................................................................................371
Appendix .................................................................................................................................373

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NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.
PREFACE

INTRODUCTION

The Council of the Association of Accountancy Bodies in West Africa (ABWA) recognized the
difficulty of students when preparing for the Accounting Technicians Scheme West Africa
examinations. One of the major difficulties has been the non-availability of study materials
purposely written for the Scheme. Consequently, students relied on text books written in
economic and socio-cultural environments quite different from the West African environment.

AIM OF THE STUDY PACK
In view of the above, the quest for good study materials for the subjects of the examinations and
the committee of the ABWA Council to bridge the gap in technical accounting training in West
Africa led to the production of this Study Pack.
The Study Pack assumes a minimum prior knowledge and every chapter reappraises basic
methods and ideas in line with the syllabus.

READERSHIP
The Study Pack is primarily intended to provide comprehensive study materials for students
preparing to write the ATSWA examination.

Other beneficiaries of the Study Pack include candidates of other Professional Institutes, students
of Universities and Polytechnics pursuing first degree and post graduate studies in Accounting,
advanced degrees in Accounting as well as Professional Accountants who may use the Study
Pack as reference materials.

APPROACH
The Study Pack has been designed for independent study by students and as concepts have been
developed methodically or as a text to be used in conjunction with tuition at schools and colleges.
The Study Pack can effectively be used as course text and for revision. It is recommended that
readers have their own copies.
ix
NOTE: This is a work in progress. All topics in the syllabus are covered but editing for necessary
corrections is in progress.
Thanks.

STRUCTURE OF THE STUDY PACK
The layout of the chapters has been standardised so as to present information in a simple form that
is easy to assimilate.

The Study Pack is organised into chapters. Each chapter deals with a particular area of the
subject, starting with learning objective and a summary of sections contained therein.

The introduction also gives specific guidance to the reader based on the contents of the current
syllabus and the current trends in examinations. The main body of the chapter is subdivided into
sections to make for easy and coherent reading. However, in some chapters, the emphasis is on
the principles or applications while others emphasise methods and procedures.

At the end of each chapter is found the following
 Summary
 Points to note (these are used for purpose of emphasis or clarification)
 Examination type questions and;
 Suggested answers

HOW TO USE THE STUDY PACK
Students are advised to read the Study Pack and attempt the questions before checking the
suggested answers.

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