Quantitative techniques in business, management and finance: a case-study approach

503 Pages·2017·12.54 MB·English

by  Awari

Quantitative Techniques in
Business, Management and Finance
A Case-Study Approach
Quantitative Techniques in
Business, Management and Finance
A Case-Study Approach
Umeshkumar Dubey
Tulsiramji Gaikwad-Patil College of Engineering & Technology
Nagpur, Maharashtra State, India
D P Kothari
S B Jain Institute of Technology, Management & Research
Nagpur, Maharashtra State, India
G K Awari
Tulsiramji Gaikwad-Patil College of Engineering & Technology
Nagpur, Maharashtra State, India
Quantitative Techniques in
Business, Management and Finance
A Case-Study Approach
Umeshkumar Dubey
Tulsiramji Gaikwad-Patil College of Engineering & Technology
Nagpur, Maharashtra State, India
D P Kothari
S B Jain Institute of Technology, Management & Research
Nagpur, Maharashtra State, India
G K Awari
Tulsiramji Gaikwad-Patil College of Engineering & Technology
Nagpur, Maharashtra State, India
CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Dubey, Umeshkumar, author. | Kothari, D. P. (Dwarkadas Pralhaddas),
1944- author. | Awari, G. K., author.
Title: Quantitative techniques in business, management and finance : a
case-study approach / Umeshkumar Dubey, D P Kothari, and G K Awari.
Description: Boca Raton : Chapman & Hall/CRC, 2016. | Includes
bibliographical references and index.
Identifiers: LCCN 2016022252 | ISBN 9781498769464 (alk. paper)
Subjects: LCSH: Business enterprises--Finance. | Decision
making--Methodology. | Quantitative research.
Classification: LCC HG4026 .D83 2016 | DDC 650.072/1--dc23
LC record available at https://lccn.loc.gov/2016022252
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K29302_Book.indb 4 03/10/16 8:09 PM
Contents
Preface ...........................................................................................................................................xxi
Acknowledgements ..................................................................................................................xxiii
Authors ........................................................................................................................................xxv
1. Quantitative Decision Making – An Overview ...............................................................1
1.1 Introduction ...................................................................................................................1
1.2 Meaning of Quantitative Techniques .........................................................................2
1.2.1 Concept of Statistics .........................................................................................2
1.2.2 Concept of Operations Research ...................................................................2
1.3 Evolution of Quantitative Techniques ........................................................................2
1.4 Classification of Quantitative Methods .....................................................................3
1.5 Data Collection ..............................................................................................................4
1.5.1 Statistical Data ..................................................................................................4
1.5.2 Statistical Methods ..........................................................................................4
1.5.3 Data Collection .................................................................................................4
1.5.4 Organisation of Data .......................................................................................4
1.6 Characteristics of Data .................................................................................................4
1.7 Types of Statistical Data ...............................................................................................5
1.7.1 Arriving at the Solution ..................................................................................5
1.7.2 Presentation ......................................................................................................6
1.7.3 Analysis .............................................................................................................6
1.7.4 Interpretation ....................................................................................................6
1.8 Classification of Quantitative Techniques .................................................................6
1.8.1 Descriptive Statistics .......................................................................................7
1.8.2 Inductive Statistics ...........................................................................................7
1.8.3 Statistical Decision Theory .............................................................................7
1.9 Methodology of Quantitative Techniques .................................................................8
1.9.1 Steps ...................................................................................................................8
1.10 Various Statistical Methods .........................................................................................8
1.10.1 Measure of Central Tendency ........................................................................8
1.10.1.1 Mean ...................................................................................................8
1.10.1.2 Median ...............................................................................................9
1.10.1.3 Mode...................................................................................................9
1.10.2 Measures of Dispersion ..................................................................................9
1.10.3 Correlation ........................................................................................................9
1.10.4 Regression Analysis ........................................................................................9
1.10.5 Time-Series Analysis .......................................................................................9
1.10.6 Index Numbers ...............................................................................................10
1.10.7 Sampling and Statistical Inference ..............................................................10
1.10.7.1 Random Sampling ..........................................................................10
1.10.7.2 Non-Random Sampling .................................................................10
1.11 Advantages of Quantitative Methods ......................................................................11
1.11.1 Definiteness ....................................................................................................11
1.11.2 Condensation ..................................................................................................11
v
vi Contents
1.11.3 Comparison ....................................................................................................11
1.11.4 Policy Formulation .........................................................................................12
1.11.5 Hypothesis Testing ........................................................................................12
1.11.6 Prediction ........................................................................................................12
1.12 Application of Quantitative Techniques in Business Management ....................12
1.12.1 Management ...................................................................................................12
1.12.1.1 Marketing Management ................................................................12
1.12.1.2 Production Management ...............................................................12
1.12.1.3 Finance Management .....................................................................12
1.12.1.4 Personnel Management .................................................................13
1.12.2 Economics .......................................................................................................13
1.12.3 Research and Development ..........................................................................13
1.12.4 Natural Science ..............................................................................................13
1.13 Limitations of Quantitative Techniques ..................................................................13
1.14 Summary ......................................................................................................................14
2. Arranging Data .....................................................................................................................17
2.1 Meaning of Data ..........................................................................................................17
2.2 Types of Data ...............................................................................................................17
2.2.1 Published Data ...............................................................................................17
2.2.1.1 Published Sources ..........................................................................17
2.2.2 Unpublished Data ..........................................................................................17
2.2.2.1 Unpublished Sources .....................................................................18
2.2.3 Primary Data ..................................................................................................18
2.2.3.1 Editing Primary Data ....................................................................18
2.2.4 Secondary Data ..............................................................................................19
2.2.4.1 Precautions in the Use of Secondary Data..................................19
2.3 Primary versus Secondary Data ...............................................................................19
2.4 Classification of Data ..................................................................................................20
2.4.1 Methods of Classification .............................................................................20
2.4.1.1 Geographical Classification ..........................................................20
2.4.1.2 Chronological Classification .........................................................20
2.4.1.3 Qualitative Classification ..............................................................21
2.4.1.4 Quantitative Classification ............................................................21
2.5 Data Collection ............................................................................................................21
2.5.1 Population .......................................................................................................21
2.5.2 Sample .............................................................................................................21
2.5.3 Testing the Validity of Data ..........................................................................21
2.5.4 Complete Enumeration or Census Survey or Census ..............................22
2.5.5 Sample Method ..............................................................................................22
2.5.6 Methods of Collecting Primary Data ..........................................................22
2.5.6.1 Observation Method ......................................................................22
2.5.6.2 Personal Interviews ........................................................................22
2.5.6.3 Questionnaire Method ..................................................................22
2.6 Data Presentation Devices .........................................................................................24
2.6.1 Tables ...............................................................................................................24
2.6.2 Tabulation .......................................................................................................24
2.6.3 Uses of Tabulation..........................................................................................24
2.6.4 Objectives of Tabulation................................................................................24
Contents vii
2.6.5 Parts of an Ideal Table ...................................................................................25
2.7 Graphs ...........................................................................................................................25
2.7.1 Types of Graphs or Charts ............................................................................25
2.7.1.1 Rules for Constructing the Line Graph .......................................25
2.7.1.2 Bar Chart .........................................................................................26
2.7.1.3 Pie Diagram .....................................................................................27
2.8 Frequency Distribution ..............................................................................................28
2.8.1 Discrete Frequency Distribution .................................................................28
2.8.2 Continuous Frequency Distribution ...........................................................29
2.8.2.1 Types of Class Interval ..................................................................29
2.8.2.2 Selection of Class Intervals ...........................................................30
2.8.3 Cumulative Frequencies ...............................................................................30
2.8.4 Relative Frequencies ......................................................................................30
2.9 Histogram ....................................................................................................................30
2.9.1 Relative Frequency Histogram ....................................................................31
2.9.2 Absolute Histogram ......................................................................................32
2.9.3 Difference between a Relative Frequency Histogram and an
Absolute Histogram ......................................................................................32
2.10 Frequency Polygon ......................................................................................................32
2.11 Frequency Curve .........................................................................................................33
2.12 Cumulative Frequency Distribution ........................................................................34
2.12.1 Ogive or Cumulative Frequency Curve ......................................................34
2.12.1.1 Less than Ogive ..............................................................................34
2.12.1.2 More than Ogive .............................................................................35
2.13 Skewness and Kurtosis ..............................................................................................36
2.13.1 Skewness .........................................................................................................36
2.13.1.1 Symmetrical Curves.......................................................................36
2.13.1.2 Skewed Curve .................................................................................36
2.13.1.3 Positively Skewed Curve ...............................................................37
2.13.1.4 Negatively Skewed Curve .............................................................37
2.13.2 Kurtosis ...........................................................................................................37
2.14 Summary ......................................................................................................................37
3. Measures of Central Tendency ..........................................................................................39
3.1 Introduction .................................................................................................................39
3.2 Significance of Measures of Central Tendency .......................................................39
3.3 Properties of Good Measures of Central Tendency ...............................................40
3.4 Arithmetic Mean .........................................................................................................40
3.4.1 Calculating the Mean from Ungrouped Data............................................40
3.4.2 Mathematical Properties of Arithmetic Mean ...........................................47
3.4.3 Weighted Arithmetic Mean ..........................................................................48
3.5 Median ..........................................................................................................................50
3.5.1 Calculating the Median from Ungrouped Data ........................................51
3.5.2 Mathematical Properties of Median ...........................................................55
3.6 Quantiles ......................................................................................................................56
3.6.1 Quartiles ..........................................................................................................56
3.6.2 Deciles .............................................................................................................56
3.6.3 Percentiles .......................................................................................................56
3.7 Mode .............................................................................................................................58
viii Contents
3.8 Relationship among Mean, Median and Mode ......................................................61
3.9 Comparison of Mean and Median ...........................................................................62
3.10 Geometric Mean ..........................................................................................................62
3.11 Harmonic Mean ..........................................................................................................65
3.12 Summary ......................................................................................................................68
4. Measures of Variation and Skewness ..............................................................................71
4.1 Introduction .................................................................................................................71
4.1.1 Significance of Measuring Variation ...........................................................71
4.1.2 Absolute versus Relative Measures of Variation .......................................71
4.2 Range ............................................................................................................................72
4.2.1 For Ungrouped Data ......................................................................................72
4.2.2 For Grouped Data ..........................................................................................72
4.2.3 Coefficient of Range .......................................................................................73
4.2.4 Interquartile Range ........................................................................................74
4.2.4.1 Need for Interquartile Range .......................................................74
4.2.4.2 Definition of Interquartile Range.................................................74
4.2.5 Semi-Interquartile Range or Quartile Deviation ......................................74
4.2.5.1 For Ungrouped Data ......................................................................75
4.2.5.2 For Grouped Data ...........................................................................75
4.2.5.3 Coefficient of Quartile Deviation .................................................76
4.3 Mean Deviation or Average Deviation ....................................................................79
4.3.1 Discrete Series ................................................................................................80
4.3.2 Continuous Series ..........................................................................................82
4.4 Standard Deviation .....................................................................................................87
4.4.1 Individual Series ............................................................................................87
4.4.2 Discrete Series ................................................................................................88
4.4.3 Step Deviation Method .................................................................................89
4.4.4 Continuous Series ..........................................................................................90
4.5 Variance ........................................................................................................................91
4.5.1 For Grouped and Ungrouped Data .............................................................91
4.6 Coefficient of Variation ...............................................................................................92
4.7 Bienayme–Chebyshev Rule .......................................................................................96
4.7.1 Statement of the Bienayme–Chebyshev Rule ............................................96
4.7.2 Application ......................................................................................................96
4.8 Skewness ......................................................................................................................97
4.8.1 Relative Skewness ..........................................................................................98
4.9 Summary ......................................................................................................................99
5. Probability Theory .............................................................................................................103
5.1 Introduction ...............................................................................................................103
5.2 Basic Concepts ...........................................................................................................104
5.2.1 Experiment ....................................................................................................104
5.2.2 Random Experiment ...................................................................................104
5.2.3 Outcome ........................................................................................................104
5.2.4 Sample Space ................................................................................................104
5.2.5 Event ..............................................................................................................104
Contents ix
5.2.6 Certain Event ................................................................................................104
5.2.7 Impossible Event ..........................................................................................105
5.2.8 Compound Event .........................................................................................105
5.2.9 Complement of an Event .............................................................................105
5.2.10 Mutually Exclusive Events..........................................................................105
5.2.11 Independent Events .....................................................................................105
5.2.12 Dependent Events ........................................................................................106
5.2.13 Exhaustive Events ........................................................................................106
5.2.14 Favourable Event ..........................................................................................106
5.2.15 Equally Likely Event....................................................................................106
5.2.16 Sample Spaces...............................................................................................106
5.3 Probability ..................................................................................................................106
5.3.1 Classical Probability ....................................................................................107
5.3.1.1 Definition of Classical Probability .............................................107
5.3.2 Relative Frequency.......................................................................................108
5.3.2.1 Relative Frequency of Occurrence Approach ..........................108
5.3.3 Limitation of the Classical Approach .......................................................109
5.3.3.1 Limitations of Classical Approach to Probability ...................109
5.3.4 Subjective Probability ..................................................................................110
5.3.5 Marginal or Unconditional Probability ....................................................110
5.3.6 Empirical Probability ..................................................................................110
5.4 Probability Rules .......................................................................................................110
5.4.1 Additional Rule (Mutually Exhaustive Events) .......................................112
5.4.1.1 Addition Theorem ........................................................................112
5.4.1.2 Sample Space .................................................................................112
5.4.2 Additional Rule (Not Mutually Exhaustive Events) ...............................113
5.4.2.1 Multiplication Theorem ...............................................................113
5.4.3 Multiplication Rule (Independent Events) ...............................................114
5.4.4 Multiplication Rule (Dependent Events) ..................................................114
5.4.5 Axioms to Probability .................................................................................115
5.4.6 Addition Theorem .......................................................................................115
5.4.7 Multiplication Theorem ..............................................................................115
5.5 Conditional Probability ............................................................................................116
5.5.1 Dependent Events ........................................................................................117
5.5.2 A Priori or Prior Probability .......................................................................118
5.5.3 Posterior or Revised Probability ................................................................118
5.5.4 Bayes’ Theorem ............................................................................................118
5.5.5 Application of Bayes’ Theorem ..................................................................119
5.6 Set Theory ..................................................................................................................123
5.6.1 Power of Set ..................................................................................................123
5.6.2 Elementary Concepts of Set ........................................................................123
5.6.2.1 Universal Set .................................................................................123
5.6.2.2 Subset of a Set ...............................................................................123
5.6.2.3 Equality of Two Sets .....................................................................124
5.6.2.4 Complement of a Set ....................................................................124
5.6.2.5 Difference of Two Sets .................................................................124
5.6.2.6 Cardinal Number of a Finite Set ................................................125
5.6.3 Operations of Sets ........................................................................................125