STATISTICSfor

Business and Economics

Fifth Edition

Vikas® Publishing House Pvt Ltd

STATISTICSfor

Business and Economics

Fifth Edition

R P HoodaEx-Professor of CommerceKurukshetra University

Statistics for Business and EconomicsISBN: 978-93-259-6120-3

First published by Vikas Publishing House 2013Fifth Edition 2013

Vikas® is the registered trademark of Vikas Publishing House Pvt LtdCopyright © R P Hooda

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Dedicatedto

you

The book continues to be dedicated to you for your affinity, howsoever far or near you may be.

PrefaceRight since its fi rst edition which came in 1993, this text has continued to grow popular with the readers, both students and teachers. Encouraged by the suggestions received, the last edition of the book has been extensively revised to strengthen it further with a focus on the applicational aspects of the methods discussed.

This fi fth edition of the book is expected to cater to the needs of the students in a much better way on account of the following:

The presentation of the subject matter has been made extremely interest-focused, more objective, and concise. Paragraphic linkages and explanations have been further strengthened and simplified.

The emphasis on evolving and discussing the various statistical methods has been made more subtle. The notational and symbolic expressions have been clearly introduced in the very beginning to make subsequent statement of formulae more learner-friendly.

Review questions and problems have been doubled to provide a rich inventory of solved and unsolved problems. This would enable the students to have an intuitive understanding of various methods and their application to real life situations.

Additions, among others, on data collection and presentation, prelude to probability, statistical inferences in relation to correlation and regression, and quite a few more non-parametric tests have greatly enhanced the usefulness of the book.

Thus, on the whole, the book has become richer both in content and presentation so as to expose the learners to the essentials of the subject without requiring much of formal help. A close reading enables an enthusiastic reader in developing the basic statistical sense, even if he/she has no prior exposure to the subject.

In tone, tenor, and presentation, the book is now much more reader-friendly, more attuned to allaying the learners’ initial fear of the subject, and facilitating easy grasp of the various formulae.

In this endeavour, a special gratitude is due to all those who cared to send their suggestions for further improvement of the book. Gratitude is always also due to the UGC for the seed money provided to meet the part expenses of bringing out its fi rst edition, and to the NBT for adopting it for subsidy.

Among colleagues and friends, the contribution of Prof S Kaushal deserves special mention for meticulously editing the earlier drafts. Credit also goes to Dr Ramesh Dalal for providing willing assistance whenever needed and Gulshan Taneja, Professor, Department of Mathematics, MDU, Rohtak for necessary checking, rechecking & evaluation.

R P HOODA

ContentsPreface vii

1 DEFINING STATISTICS Scope and Related Issues 1.1 Statistics Defined 1 1.2 Meaning Restated 1 1.3 Two Major Divisions of Statistics 2 1.3.1 Descriptive Statistics 2 1.3.2 Inferential Statistics 2 1.4 Statistics and Risk Evaluation 3 1.5 Some Other Issues 3 1.6 Scope Revisited 4 1.7 Types of Data 4 1.7.1 Quantitative Data and Types 4 1.7.2 Qualitative Data and Types 5 1.8 Secondary and Primary Data 5 1.9 Evaluating Statistics 6 1.10 The Language of Statistics 7 1.10.1 Notations for Variables 7 1.10.2 Notations for Observed Data 7 1.10.3 Notations in Sampling 7 1.10.4 Notations for Sample Statistics 8 1.11 S Sigma Operation 8 1.12 Rules of S Operation 8 Solve the following 10 Answer the following 10

2 STATISTICAL DATA Collection and Presentation 2.1 Data Collection 11 2.2 Issues in Secondary Data Collection 11 2.2.1 Sources of Secondary Data 11 2.2.2 Evaluating Secondary Data 12 2.3 Issues in Primary Data Collection 13 2.3.1 Population vs Sample Survey 13 2.3.2 Techniques of Data Collection 13 2.3.3 Preparing a Questionnaire 14 2.3.4 Pre-Testing and Editing 15 2.4 Presentation of Data 15 2.5 Tabular Presentation 16 2.5.1 Types of Tables 16 2.5.2 Components of a Table 17 2.5.3 How to Frame Tables 17 2.5.4 A Contingency Table 18 2.6 Graphic Presentation 19 2.6.1 Types of Graphs 19 Solve the following 23 Answer the following 24

3 SUMMARIZING DATA Concepts, Issues, and Procedure 3.1 Defining the Task 25 3.2 Raw Data 25

x | Contents

3.3 An Ordered Array 26 3.4 A Frequency Distribution 26 3.5 Constructing a Frequency Distribution 26 3.5.1 Tally Method 26 3.5.2 Entry Form Method 27 3.6 Types of Frequency Distributions 28 3.7 More on Distributions 28 3.8 Concerns in Constructing a Frequency Distribution 28 3.8.1 Number of Classes 28 3.8.2 Width of the Class Interval(s) 29 3.8.3 Establishing the Initial Class 29 3.8.4 Stated and Real Class Limits 30 3.9 Other Issues 31 3.9.1 Unequal Class Intervals 31 3.9.2 Open-ended Class Intervals 31 3.10 Graphic Presentation of a Frequency Distribution 31 3.11 Histogram 31 3.11.1 For Equal Class Intervals 31 3.11.2 For Unequal Class Intervals 32 3.12 Frequency Polygon 32 3.13 Comparing Frequency Distributions 33 3.14 Smoothing a Frequency Polygon 33 3.15 Frequency Distribution Models 34 3.16 A Cumulative Frequency Curve (or an Ogive) 35 Answer the following 36

4 SUMMARY MEASURES -1 Measures of Central Tendency 4.1 Central Tendency 38 4.2 Measures of Central Tendency 38 4.3 Arithmetic Mean, and its Computation 38 4.3.1 Correction for Wrong Entries 40 4.3.2 Properties of Arithmetic Mean 41 4.3.3 More Efficient Method(s) Restated 44 4.3.4 Weighted Arithmetic Mean/Average 45 4.4 Median, and its Computation 46 4.4.1 Properties of Median 47 4.4.2 Locating Median from an Ogive 48 4.5 Mode, and its Computation 48 4.5.1 Properties of Mode 49 4.6 Relationship Among Mean, Median, and Mode 49 4.7 The Three Measures Compared 51 4.8 Geometric Mean, and its Computation 51 4.8.1 Weighted Geometric Mean 52 4.8.2 Combined Geometric Mean 53 4.8.3 Computation of Compound Interest Rate 53 4.9 Harmonic Mean, and its Computation 54 4.9.1 Weighted Harmonic Mean 55 4.9.2 xw and HMw Compared 56 4.10 Partition Values 58 4.10.1 Quartiles 58 4.10.2 Deciles 59 4.10.3 Percentiles 59

Contents | xi

Review Problems 60 Solve the following 76 Answer the following 80

5 SUMMARY MEASURES - II Measures of Dispersion 5.1 Dispersion Defined 81 5.2 Measures of Dispersion 81 5.3 The Range, and How to Obtain It 82 5.4 Quartile Deviation, and Computation 82 5.5 Mean Absolute Deviation, and Computation 83 5.6 Variance, and Computation 84 5.6.1 The Alternative Easier Method 85 5.6.2 The Efficient Method 87 5.6.3 Properties of Variance 88 5.6.4 Sample Variance for Estimating σ 2 90 5.7 Standard Deviation, and Computation 90 5.7.1 Applications of Standard Deviation 90 5.7.2 Chebyschev’s Theorem 91 5.7.3 Sheppard’s Correction 91 5.8 Empirical Relationship 91 5.9 Relative Measures of Dispersion 92 5.9.1 Coefficient of Quartile Deviation 92 5.9.2 Coefficient of Mean Absolute Deviation 92 5.9.3 Coefficient of Variation 92 5.10 Measures of Dispersion Compared 92 5.11 Moments 92 5.11.1 Moments about the Origin 93 5.11.2 Moments about the Mean 93 Review Problems 94 Solve the following 104 Answer the following 106

6 SUMMARY MEASURES - III Skewness and Kurtosis 6.1 Skewness, and Measures 107 6.1.1 Pearsonian Measure of Skewness 107 6.1.2 Bowley’s Measure of Skewness 108 6.1.3 Kelly’s Measure of Skewness 109 6.1.4 Moment Coefficient of Skewness 109 6.2 Kurtosis, and Measures 109 6.2.1 Moment Coefficient of Kurtosis 110 6.2.2 Percentile Coefficient of Kurtosis 110 Review Problems 111 Solve the following 115 Answer the following 116

7 REGRESSION AND CORRELATION -1 The Two-Variable Linear Case 7.1 Regression and Correlation 117 7.2 Types of Relationship 117 7.3 Linear Regression 118 7.3.1 The Scatter Diagram 118

xii | Contents

7.3.2 Fitting a Straight Line 119 7.3.3 Methods of Fitting a Straight Line 120 7.3.4 Determining the Constants 120 7.3.5 Obtaining the Best Fit 124 7.4 Predicting an Estimate, and its Preciseness 124 7.5 Measuring the Error of Estimate(s) 125 7.5.1 The Alternative Method 126 7.5.2 Interpretations of SY.X 126 7.6 Regression of X on Y 127 7.7 Regression and Causality 128 7.8 Regression and Extrapolation 128 7.9 SY.X as a Measure of Correlation 128 7.10 Coefficient of Determination (A Link between Correlation and Regression) 129 7.10.1 Interpretations of the Coefficient of Determination 132 7.10.2 Relation between SY.X and r 132 7.11 Correlation Reconsidered 133 7.12 Product Moment Formula for Computing r 133 7.13 Computation of r (Cross-Classification Table) 136 7.14 Correlation of Ranks rs 138 7.14.1 Rank Correlation in the Case of Tied Ranks 140 7.15 Statistical Inferences and Regression and Correlation 141 Review Problems 141 Solve the following 152 Answer the following 155

8 REGRESSION AND CORRELATION - II The Three-Variable Linear Case 8.1 Linear Regression Equation 157 8.1.1 The Three Normal Equations 158 8.1.2 Regression Equation Simplified 159 8.2 Regression Equation in Terms of Simple Correlation Coefficients 161 8.3 Standard Error of Estimate 164 8.3.1 S1.2 and S1.23 Compared 165 8.4 Multiple Correlation 165 8.5 Partial Correlation 167 Review Problems 168 Solve the following 176 Answer the following 177

9 INDEX NUMBERS Price, Quantity, and Value Indices 9.1 Index Number as a Concept 178 9.2 Types of Index Numbers 178 9.3 Notations Used 179 9.4 Price (Quantity) Relatives 179 9.5 Simple Index Numbers 180 9.6 Simple Aggregative Price (Quantity) Indices 181 9.6.1 Index of Simple Aggregative Prices (Quantities) 181 9.6.2 Index of Average of Price (Quantity) Relatives 182 9.7 Weighted Aggregative Price (Quantity) Indices 184 9.7.1 Those Using Base Period Quantities (Prices) as Weights 184 9.7.2 Those Using Given Period Quantities (Prices) as Weights 185 9.7.3 Relationship between Laspeyre’s and Paasche ‘s Indices 186 9.7.4 More on the Two Indicies 189

Contents | xiii

9.8 Other Aggregative Indices 190 9.8.1 Marshall-Edgeworth Index 190 9.8.2 Bowley’s Index 190 9.8.3 Fisher’s Ideal Index 190 9.9 Indices of Weighted Average of Price/Quantity Relatives 191 9.10 Tests of Adequacy of Index Numbers 194 9.10.1 Time Reversal Test 194 9.10.2 Factor Reversal Test 194 9.11 Shifting the Base and Splicing 195 9.11.1 Shifting the Base 195 9.11.2 Splicing Two Index Series 196 9.12 Chain Base Indices 197 9.13 Uses of Index Numbers 197 9.14 Problems in Constructing Index Numbers 197 Review Problems 198 Solve the following 206 Answer the following 209

10 TIME SERIES ANALYSIS Components and Decomposition 10.1 Meaning and Need 211 10.2 Time Series Graphs 211 10.2.1 Logarithmic Charts 212 10.3 Four Types of Variations 212 10.4 Components Characterized 213 10.4.1 Secular Trend 213 10.4.2 Cyclical Variations 213 10.4.3 Seasonal Variations 213 10.4.4 Random Variations 214 10.5 Approaches to Time Series Analysis 214 10.5.1 The Additive Approach 214 10.5.2 The Multiplicative Approach 214 10.6 Adjusting the Time Series 215 10.7 The Process of Decomposition 216 10.8 Estimating Trend Variations 216 10.8.1 Methods of Estimating Straight-Line Trend 216 10.9 Second Degree Polynomial Trend 221 10.10 Exponential Trend 222 10.11 Detrending a Time Series 224 10.12 Estimating Seasonal Variations 225 10.12.1 Methods of Constructing Seasonal Index 225 10.13 Adjusting Time Series for Seasonal Variations 231 10.14 Seasonal Index and Future Estimation 232 10.15 Estimating Cyclical Variations 232 Review Problems 233 Solve the following 246 Answer the following 248

11 BUSINESS FORECASTING A Brief on Issues and Techniques 11.1 Importance of Business Forecasting 249 11.2 Scope of Forecasting 250

xiv | Contents

11.3 Types of Forecasting 250 11.3.1 Long-Term Forecasting 250 11.3.2 Short-Term Forecasting 250 11.4 Approach to Forecasting 251 11.5 Forecasting Techniques 251 11.6 Naive Method 251 11.7 Trend Projection (Long-Term Forecasting) 252 11.8 Predicting Business Cycles (Short-Term Forecasting) 253 11.9 Business Indicators 254 11.10 Diffusion Index 254 11.11 Lead-Lag Relationships 255 11.12 Factor-Listing Approach 256 11.13 Regression Analysis 256 11.14 Judgemental Methods 256 11.15 Market Surveys and Tests 257 11.16 Industry vs Company Forecasts 257 11.17 External and Internal Factors Affecting Company Sales 258 11.18 Reliability of Forecasts 258 Answer the following 258

12 A PRELUDE TO PROBABILITY Concepts, Definitions, and Postulates 12.1 Need and Relevance 259 12.2 Related Terms and Concepts 260 12.2.1 A Trial and an Experiment 260 12.2.2 Sample Points and Sample Space 260 12.2.3 A Generalization 261 12.2.4 Random Sampling 261 12.3 Events 261 12.3.1 Types of Event 262 12.3.2 Rules of Event Operations 262 12.4 Methods of Counting Sample Points 263 12.4.1 The Fundamental Principle 263 12.4.2 Permutations 263 12.4.3 Set Partitioning 265 12.4.4 Combinations 265 12.5 The Three Approaches to Defining Probability 266 12.6 Basic Probability Postulates 268 Review Problems 268 Solve the following 270 Answer the following 271

13 THE BASIC PROBABILITY RULES And Bayesian Theorem 13.1 The Additive Rules 273 13.1.1 Additive Rule I 273 13.1.2 Additive Rule II 274 13.2 The Complementation Rule 276 13.3 The Conditional Probability Rules 276 13.4 Joint and Marginal Probabilities 281 13.5 The Multiplication Rules 281 13.5.1 Multiplication Rule I 281 13.5.2 Multiplication Rule II 283

Statistics For Business And Economics

Publisher : SChand Publications ISBN : 9789325961203 Author : R P Hooda

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