Business StatisticsFourth Edition

J. K. SharmaProfessor

Amity Business School,Amity University, Noida

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Business StatisticsISBN: 978-93259-8081-5

Fourth Edition 2014

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Contents

Preface to the Fourth Edition xvPreface to the First Edition xvii

CHAPTER 1 STATISTICS: AN OVERVIEW 1–22

1.1 Reasons for Learning Statistics 11.2 Growth and Development of Statistics 21.3 Statistical Thinking and Analysis 21.4 Statistics Defined 31.5 Types of Statistical Methods 41.6 Importance and Scope of Statistics 5 1.6.1 Statistics and State 5 1.6.2 Statistics in Economics 5 1.6.3 Statistics in Business Management 6 1.6.4 Statistics in Physical Sciences 6 1.6.5 Statistics in Social Sciences 6 1.6.6 Statistics in Medical Sciences 7 1.6.7 Statistics and Computers 71.7 Limitations of Statistics 7 1.7.1 Statistics Does Not Study Qualitative Phenomena 7 1.7.2 Statistics Does Not Study Individuals 7 1.7.3 Statistics Can Be Misused 71.8 How to Lie with Statistics? 8Conceptual Questions 1A 81.9 Need for Data 9 1.9.1 Types of Data 91.10 Principles of Measurement 101.11 Sources of Data 12 1.11.1 Primary Data Sources 13 1.11.2 Secondary Data Sources 19Conceptual Questions 1B 21Chapter Concepts Quiz 22

CHAPTER 2 DATA CLASSIFICATION, TABULATION AND PRESENTATION 23–75

2.1 Introduction 232.2 Classification of Data 23 2.2.1 Requisites of Ideal Classification 24 2.2.2 Basis of Classification 242.3 Organizing Data Using Data Array 25 2.3.1 Frequency Distribution 26 2.3.2 Methods of Data Classification 29 2.3.3 Bivariate Frequency Distribution 33 2.3.4 Types of Frequency Distributions 35

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Conceptual Questions 2A 37Self-practice Problems 2A 37Hints and Answers 382.4 Tabulation of Data 39 2.4.1 Meaning and Definition 39 2.4.2 Objectives of Tabulation 39 2.4.3 Parts of a Table 40 2.4.4 Types of Tables 41 2.4.5 General and Summary Tables 42Conceptual Questions 2B 46Self-practice Problems 2B 46Hints and Answers 472.5 Graphical Presentation of Data 49 2.5.1 Functions of a Graph 49 2.5.2 Advantages and Limitations of Diagrams (Graphs) 49 2.5.3 General Rules for Drawing Diagrams 502.6 Types of Diagrams 50 2.6.1 One-dimensional Diagrams 51 2.6.2 Two-dimensional Diagrams 62 2.6.3 Three-dimensional Diagrams 65 2.6.4 Pictograms or Ideographs 65 2.6.5 Cartograms or Statistical Maps 662.7 Exploratory Data Analysis 66 2.7.1 Stem-and-Leaf Displays 66Conceptual Questins 2C 68Self-practice Problems 2C 68Hints and Answers 70Formulae Used 70Chapter Concepts Quiz 71Review Self-practice Problems 72Case Studies 74

CHAPTER 3 MEASURES OF CENTRAL TENDENCY 76–125

3.1 Introduction 763.2 Objectives of Averaging 773.3 Requisites of a Measure of Central Tendency 773.4 Measures of Central Tendency 773.5 Mathematical Averages 78 3.5.1 Arithmetic Mean of Ungrouped Data 78 3.5.2 Arithmetic Mean of Grouped Data 81 3.5.3 Some Special Types of Problems and Their Solutions 84 3.5.4 Weighted Arithmetic Mean 90 3.5.5 Advantages and Disadvantages of Arithmetic Mean 92Conceptual Questions 3A 93Self-practice Problems 3A 93Hints and Answers 953.6 Geometric Mean 95 3.6.1 Combined Geometric Mean 97 3.6.2 Weighted Geometric Mean 97 3.6.3 Advantages, Disadvantages and Applications of G.M. 98Conceptual Questions 3B 99Self-practice Problems 3B 99Hints and Answers 1003.7 Harmonic Mean 101 3.7.1 Advantages, Disadvantages and Applications of H.M. 1013.8 Relationship Among A.M., G.M. and H.M. 102Self-practice Problems 3C 102Hints and Answers 1023.9 Averages of Position 102

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3.9.1 Median 103 3.9.2 Advantages and Disadvantages of Median 1053.10 Partition Values — Quartiles, Deciles and Percentiles 105 3.10.1 Graphical Method for Calculating Partition Values 106Conceptual Questions 3C 110Self-practice Problems 3D 110Hints and Answers 1113.11 Mode 111 3.11.1 Graphical Method for Calculating Mode Value 114 3.11.2 Advantages and Disadvantages of Mode Value 1143.12 Relationship Between Mean, Median and Mode 1143.13 Comparison Between Measures of Central Tendency 115Conceptual Questions 3D 116Self-practice Problems 3E 116Hints and Answers 118Formulae Used 118Chapter Concepts Quiz 119Review Self-practice Problems 120Hints and Answers 122Case Studies 124

CHAPTER 4 MEASURES OF DISPERSION 126–162

4.1 Introduction 1264.2 Significance of Measuring Dispersion 127 4.2.1 Requisites for a Good Measure of Variation 1284.3 Classification of Measures of Dispersion 1284.4 Distance Measures 129 4.4.1 Range 129 4.4.2 Interquartile Range or Deviation 130Conceptual Questions 4A 133Self-practice Problems 4A 133Hints and Answers 1344.5 Average Deviation Measures 135 4.5.1 Mean Absolute Deviation 135 4.5.2 Variance and Standard Deviation 138 4.5.3 Mathematical Properties of Standard Deviation 142 4.5.4 Chebyshev’s Theorem 143 4.5.5 Coefficient of Variation 149Conceptual Questions 4B 151Self-practice Problems 4B 152Hints and Answers 154Formulae Used 155Chapter Concepts Quiz 155Review Self-practice Problems 157Hints and Answers 159Case Studies 162

CHAPTER 5 SKEWNESS, MOMENTS AND KURTOSIS 163–185

5.1 Introduction 1635.2 Measures of Skewness 164 5.2.1 Relative Measures of Skewness 164Conceptual Questions 5A 170Self-practice Problems 5A 171Hints and Answers 1725.3 Moments 173 5.3.1 Moments About Mean 174 5.3.2 Moments About Arbitrary Point 174

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5.3.3 Moments About Zero (Origin) 174 5.3.4 Relationship Between Central Moments and Moments About an Assumed Mean 175 5.3.5 Moments in Standard Units 175 5.3.6 Sheppard’s Corrections for Moments 1765.4 Kurtosis 178 5.4.1 Measures of Kurtosis 178Conceptual Questions 5B 181Self-practice Problems 5B 181Hints and Answers 182Formulae Used 182Review Self-practice Problems 183Hints and Answers 184

CHAPTER 6 FUNDAMENTALS OF PROBABILITY 186–222

6.1 Introduction 1866.2 Concepts of Probability 186 6.2.1 Random Experiment 186 6.2.2 Sample Space 187 6.2.3 Types of Event 1886.3 Definition of Probability 189 6.3.1 Classical Approach 189 6.3.2 Relative Frequency Approach 190 6.3.3 Subjective Approach 190 6.3.4 Fundamental Rules of Probability 190 6.3.5 Glossary of Probability Terms 1916.4 Counting Rules for Determining the Number of Outcomes 191 6.4.1 Multistep Experiments 191 6.4.2 Combinations 191 6.4.3 Permutations 192Conceptual Questions 6A 193Self-practice Problems 6A 194Hints and Answers 1946.5 Rules of Probability and Algebra of Events 195 6.5.1 Rules of Addition 195 6.5.2 Rules of Multiplication 199Self-practice Problems 6B 208Hints and Answers 2096.6 Bayes’ Theorem 212Self-practice Problems 6C 214Hints and Answers 214Formulae Used 215Chapter Concepts Quiz 216Review Self-practice Problems 217Hints and Answers 219Case Studies 222

CHAPTER 7 PROBABILITY DISTRIBUTIONS 223–268

7.1 Introduction 2237.2 Probability Distribution Functions 2247.3 Cumulative Probability Distribution Function 2257.4 Expected Value and Variance of a Random Variable 227 7.4.1 Expected Value 227 7.4.2 Variance and Standard Deviation 227 7.4.3 Properties of Expected Value and Variance 227Conceptual Questions 7A 231Self-practice Problems 7A 231

CONTENTS vii

Hints and Answers 2327.5 Discrete Probability Distributions 232 7.5.1 Binomial Probability Distribution 232Conceptual Questions 7B 238Self-practice Problems 7B 238Hints and Answers 239 7.5.2 Poisson Probability Distribution 239 7.5.3 Negative Binomial Probability Distribution 245 7.5.4 Multinomial Probability Distribution 246 7.5.5 Hyper-geometric Probability Distribution 247Conceptual Questions 7C 248Self-practice Problems 7C 248Hints and Answers 2497.6 Continuous Probability Distributions 250 7.6.1 Normal Probability Distribution Function 250 7.6.2 Approximation of Binomial and Poisson Distributions to Normal Distribution 253 7.6.3 Uniform (Rectangular) Distribution 260 7.6.4 Exponential Probability Distribution 260 7.6.5 Gamma (Erlang) Distribution 260 7.6.6 Beta Distribution 261Conceptual Questions 7D 261Self-practice Problems 7D 262Hints and Answers 263Formulae Used 264Chapter Concepts Quiz 264Review Self-practice Problems 266Hints and Answers 267

CHAPTER 8 SAMPLING AND SAMPLING DISTRIBUTIONS 269–296

8.1 Introduction 2698.2 Reasons of Sample Survey 2698.3 Types of Bias During Sample Survey 270 8.3.1 Sampling and Non-sampling Errors 270 8.3.2 Measurement of Sampling Error 2718.4 Population Parameters and Sample Statistics 2718.5 Principles of Sampling 271 8.5.1 Principle of Statistical Regularity 271 8.5.2 Principle of Inertia of Large Numbers 2728.6 Sampling Methods 272 8.6.1 Probabilistic Sampling Methods 272 8.6.2 Non-random Sampling Methods 274 8.6.3 Choice of Sampling Methods 2758.7 Sampling Distributions 275 8.7.1 Standard Error of Statistic 276 8.7.2 Difference Between Population, Sample and Sampling Distributions 276Conceptual Questions 8A 2788.8 Sampling Distribution of Sample Mean 278 8.8.1 Sampling Distribution of Mean When Population Has Non-normal Distribution 278 8.8.2 Sampling Distribution of Mean When Population Has Normal Distribution 279 8.8.3 Sampling Distribution of Difference Between Two Sample Means 286Self-practice Problems 8A 288Hints and Answers 2888.9 Sampling Distribution of Sample Proportion 289 8.9.1 Sampling Distribution of the Difference of Two Proportions 290

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Self-practice Problems 8B 292Hints and Answers 292Formulae Used 293Chapter Concepts Quiz 293Review Self-practice Problems 295Hints and Answers 295

CHAPTER 9 ESTIMATION AND CONFIDENCE INTERVALS 297–318

9.1 Introduction 2979.2 Point Estimation 298 9.2.1 Properties of a Point Estimator 298 9.2.2 Drawback of Point Estimates 3009.3 Confidence Interval Estimation 3009.4 Interval Estimation of Population Mean (S Known) 301 9.4.1 Interval Estimation for Difference of Two Means 3039.5 Interval Estimation of Population mean (s Unknown) 303Self-practice Problems 9A 305Hints and Answers 3069.6 Interval Estimation for Population Proportion 306Self-practice Problems 9B 307Hints and Answers 3089.7 Estimating Sample Size 308 9.7.1 Sample Size for Estimating Population Mean 309 9.7.2 Sample Size for Estimating Population Proportion 311 9.7.3 Sample Size Determination for Finite Population 311Conceptual Questions 9A 312Self-practice Problems 9C 313Hints and Answers 313Formulae Used 313Chapter Concepts Quiz 314Review Self-practice Problems 315Hints and Answers 317

CHAPTER 10 HYPOTHESIS TESTING 319–37910.1 Introduction 31910.2 Hypothesis and Hypothesis Testing 319 10.2.1 Formats of Hypothesis 32010.3 Rationale for Hypothesis Testing 32010.4 General Procedure for Hypothesis Testing 32110.5 Direction of the Hypothesis Test 32310.6 Errors in Hypothesis Testing 324 10.6.1 Power of a Statistical Test 325Conceptual Questions 10A 32710.7 Hypothesis Testing for Population Parameters with Large Samples 328 10.7.1 Hypothesis Testing for Single Population Mean 328 10.7.2 Relationship Between Interval Estimation and Hypothesis Testing 329

10.7.3 p-value Approach to Test Hypothesis of Single Population Mean 332 10.7.4 Hypothesis Testing for Difference Between Two Population Means 335Self-practice Problems 10A 339Hints and Answers 34010.8 Hypothesis Testing for Single Population Proportion 341 10.8.1 Hypothesis Testing for Difference Between Two Population Proportions 34210.9 Hypothesis Testing for a Binomial Proportion 344Self-practice Problems 10B 346

CONTENTS ix

Hints and Answers 34610.10 Hypothesis Testing for Population Mean with Small Samples 348 10.10.1 Properties of Student’s t-Distribution 348 10.10.2 Hypothesis Testing for Single Population Mean 349 10.10.3 Hypothesis Testing for Difference of Two Population Means (Independent Samples) 353 10.10.4 Hypothesis Testing for Difference of Two Population Means (Dependent Samples) 359Self-practice Problems 10C 363Hints and Answers 36410.11 Hypothesis Testing Based on F-Distribution 366 10.11.1 Properties of F-Distribution 366 10.11.2 Comparing Two Population Variances 367Self-practice Problems 10D 369Hints and Answers 370Formulae Used 371Chapter Concepts Quiz 372Review Self-practice Problems 373Hints and Answers 376

CHAPTER 11 CHI-SQUARE AND OTHER NON-PARAMETRIC TESTS 380–426

11.1 Introduction 38011.2 Advantages and Limitations of Non-parametric Methods 38111.3 Chi-Square Distribution 381 11.3.1 Properties of c2 Distribution 382 11.3.2 Conditions for the Applications of c2 Test 38211.4 Chi-square Test-statistic 383 11.4.1 Grouping of Small Frequencies 38311.5 Applications of c2 Test 384 11.5.1 Contingency Table Analysis: Chi-Square Test of Independence 384Self-practice Problems 11A 390Hints and Answers 391 11.5.2 Chi-square Test for Goodness-of-fit 392 11.5.3 Yate’s Correction for Continuity 395Self-practice Problems 11B 398Hints and Answers 398

11.5.4 c2 Test for Population Variance 399 11.5.5 Coefficient of Contingency 401 11.5.6 Chi-square Test of Homogeneity 403Conceptual Questions 11A 40411.6 Sign Test for Paired Data 40411.7 Runs Test for Randomness 40811.8 Mann–Whitney U-Test 41011.9 Wilcoxon Matched Pairs Test 41411.10 Kruskal–Wallis Test 416Self-practice Problems 11C 418Hints and Answers 420Formulae Used 420Chapter Concepts Quiz 421Review Self-practice Problems 422Hints and Answers 424

CHAPTER 12 ANALYSIS OF VARIANCE 427–451

12.1 Introduction 42712.2 Analysis of Variance Approach 42812.3 Testing Equality of Population Means: One-way Classification 429

Business Statistics

Publisher : SChand Publications ISBN : 9789325980815 Author : J.K. Sharma

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