Table Of Content

Statistics for Business Statistics for Business Dr Perumal Mariappan, Ph.D. (Mathematics) Ph.D. (Management) Head PG Department of Actuarial Science Bishop Heber College Trichy – 620 017 CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2019 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-138-33617-9 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materi- als or the consequences of their use. 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CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identifi- cation and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Mariappan, Perumal, author. Title: Statistics for business / Perumal Mariappan. Description: Boca Raton, FL : CRC Press, 2019. Identifiers: LCCN 2019010834| ISBN 9781138336179 (hardback : alk. paper) | ISBN 9780429443244 (ebook) Subjects: LCSH: Commercial statistics. Classification: LCC HF1017 .M345 2019 | DDC 519.5--dc23 LC record available at https://lccn.loc.gov/2019010834 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com The author dedicates this book to Dr D. Paul Dhayabaran, Principal, Bishop Heber College, Trichy, for his wonderful dedicated service in establishing Bishop Heber College as the best higher education institution in the whole of India. Also the author dedicates this text to Sister Siriya Pushpam, Correspondent and Former Headmistress, St. Joseph’s Anglo Indian Girl’s H.Sc., School, Trichy for dedicating her life to the development of the society and to his lovable daughters Kumari S. B. Bhavana Sree and Kumari S. B. Bharani Shri. Contents Foreword ........................................................................................................................................xv Preface ..........................................................................................................................................xvii Acknowledgements ....................................................................................................................xix Author ...........................................................................................................................................xxi 1. Introduction to Statistics and Its Business Applications ...............................................1 1.1 Introduction ...................................................................................................................1 1.2 Is Statistics a Science? ...................................................................................................2 1.3 Application of Statistics in Business ...........................................................................2 1.3.1 The Phases of the Statistical Decision-Making Process .............................3 1.3.1.1 Study Design Phase .........................................................................3 1.3.1.2 Data Collection .................................................................................4 1.3.1.3 Data Analysis ....................................................................................4 1.3.1.4 Action on Results..............................................................................4 1.4 Responsibility of the Decision Maker ........................................................................4 1.5 Functions and Limitations of Statistics ......................................................................5 1.5.1 Functions of Statistics ......................................................................................5 1.5.2 Limitations of Statistics ...................................................................................5 1.6 Distrust of Statistics ......................................................................................................6 1.7 Nature of Statistical Law ..............................................................................................7 1.7.1 Law of Statistical Regularity ..........................................................................7 1.7.2 Law of Inertia of Large Numbers ..................................................................7 Exercise 1 ...................................................................................................................................7 2. Data Structures, Data Sources, and Data Collection .......................................................9 2.1 Introduction ...................................................................................................................9 2.2 Data Structures ..............................................................................................................9 2.2.1 Univariate Data ................................................................................................9 2.2.2 Bivariate Data .................................................................................................10 2.2.3 Multivariate Data ...........................................................................................10 2.3 Data Sources ................................................................................................................11 2.3.1 Primary Sources .............................................................................................11 2.3.2 Secondary Sources .........................................................................................11 2.3.3 Internal Source ...............................................................................................11 2.3.4 External Source ..............................................................................................11 2.4 Data Collection Inquiries ...........................................................................................12 2.4.1 Survey Design ................................................................................................13 2.4.1.1 Questionnaire Design ....................................................................14 2.4.2 Pilot Survey of the Questionnaire ...............................................................14 2.4.3 Editing Primary Data ....................................................................................15 2.4.4 Possible Errors in Secondary Data ..............................................................15 2.4.5 Census and Sampling Methods ...................................................................16 Exercise 2 ................................................................................................................................19 vii viii Contents 3. Data Presentation .................................................................................................................21 3.1 Introduction .................................................................................................................21 3.2 Classification of Data ..................................................................................................21 3.2.1 Types of Classification ...................................................................................21 3.3 Data Presentation ........................................................................................................22 3.3.1 Textual Form ...................................................................................................22 3.3.2 Tabular Form ..................................................................................................22 3.4 Types of Variables and Data ......................................................................................23 3.5 Levels of Measurement ..............................................................................................24 3.5.1 Nominal Scale ................................................................................................24 3.5.2 Ordinal Scale ..................................................................................................24 3.5.3 Interval Scale ..................................................................................................24 3.5.4 Ratio Scale .......................................................................................................25 3.6 Frequency .....................................................................................................................25 3.6.1 Frequency Distributions ...............................................................................25 3.7 Types of Class Interval ...............................................................................................26 3.8 Tally Mark ....................................................................................................................28 3.9 Construction of a Discrete Frequency Distribution ...............................................28 3.10 Construction of a Continuous Frequency Distribution .........................................29 3.11 Cumulative and Relative Frequencies ......................................................................29 3.12 Diagrammatic Representation of Data ....................................................................30 3.12.1 Advantages and Disadvantages of Diagrammatic Representation ........31 3.12.2 Types of Diagrams .........................................................................................31 3.12.2.1 Bar Diagram ..................................................................................31 3.12.2.2 Pie Diagram ...................................................................................34 3.12.2.3 Histogram, Frequency Polygon, and Frequency Curve ..........36 3.12.2.4 Frequency Polygon .......................................................................37 3.12.2.5 Frequency Curve ...........................................................................37 3.12.2.6 Ogive Curve ...................................................................................38 3.12.2.7 Line Diagram ................................................................................38 Exercise 3 .................................................................................................................................39 4. Measures of Central Tendency (MCT) .............................................................................43 4.1 Introduction .................................................................................................................43 4.2 MCT ...............................................................................................................................43 4.2.1 Properties of Best Average ............................................................................43 4.3 Arithmetic Mean .........................................................................................................44 4.3.1 Discrete Data ..................................................................................................44 4.3.2 Discrete Data with Frequency......................................................................44 4.3.3 Continuous Data with Frequency ...............................................................45 4.4 Mathematical Properties of Arithmetic Mean ........................................................46 4.5 Median ..........................................................................................................................50 4.5.1 Discrete Data ..................................................................................................51 4.5.2 Discrete Data with Frequency......................................................................51 4.5.3 Continuous Data with Frequency ...............................................................51 4.5.3.1 Relative Advantages .....................................................................52 4.5.3.2 Relative Disadvantages ................................................................52 4.5.3.3 Property of Median ......................................................................56 4.5.4 Graphical Method to Find the Median .......................................................56 Contents ix 4.6 Quartiles, Deciles and Percentiles ............................................................................58 4.7 Mode .............................................................................................................................61 4.7.1 Discrete Data ..................................................................................................61 4.7.2 Discrete Data with Frequency......................................................................61 4.7.3 Continuous Data with Frequency ...............................................................61 4.7.4 A Graphical Method to Evaluate the Mode ...............................................68 4.8 Comparison of Mean, Median, and Mode ..............................................................69 4.9 Weighted Arithmetic Mean .......................................................................................70 4.9.1 Advantages of the Weighted Mean .............................................................71 4.10 Geometric Mean ..........................................................................................................71 4.11 Harmonic Mean ..........................................................................................................72 Exercise 4 .................................................................................................................................73 5. Dispersion ..............................................................................................................................79 5.1 Introduction .................................................................................................................79 5.2 Range ............................................................................................................................79 5.3 Quartile Deviation (QD) .............................................................................................80 5.4 Coefficient of Quartile Deviation..............................................................................80 5.5 Mean Deviation ...........................................................................................................82 5.6 Standard Deviation (SD) ............................................................................................84 5.7 Relative Measures of Dispersion ..............................................................................89 Exercise 5 .................................................................................................................................93 6. Skewness, Moments, and Kurtosis ...................................................................................97 6.1 Introduction .................................................................................................................97 6.2 Dispersion and Skewness ..........................................................................................97 6.3 Moments .....................................................................................................................100 6.4 Kurtosis.......................................................................................................................102 Exercise 6 ...............................................................................................................................105 7. Correlation and Regression Analysis .............................................................................107 7.1 Introduction ...............................................................................................................107 7.2 Correlation .................................................................................................................107 7.2.1 Simple Correlation or Correlation .............................................................107 7.2.2 Rank Correlation ..........................................................................................108 7.2.3 Group Correlation ........................................................................................108 7.2.4 Assumptions for Karl Pearson’s Coefficient of Correlation ...................108 7.2.5 Limitations ....................................................................................................108 7.2.6 Properties ......................................................................................................108 7.2.7 Scatter Diagram ............................................................................................108 7.3 Karl Pearson Coefficient of Correlation .................................................................109 7.4 Coefficient of Correlation of a Grouped Data .......................................................115 7.5 Probable Error of the Coefficient of Correlation ...................................................118 7.6 Rank Correlation .......................................................................................................120 7.7 Regression Equations ...............................................................................................125 Exercise 7 ...............................................................................................................................134