Module Contributors Prof Dr Harish Singh Dr Vijay Dahiya Dr Aanchal Tehlan Dr Jyoti Dr Shashikant Pandey Course BBA G Subject Module On Quantitative Techniques Operations Research Semester II Credit 4 For students for education purpose only Module Objectives This module consists of four units related to assessment of Learning After studying this module students will be acquainted with different mathematical concepts and their applications They will get benefitted with different tools of transportation and assignment problem for solving various kind of problems This type of tools has wide range of applications in economics business engineering etc Every unit is divided into lessons according to the content of each unit Unit I In this unit you will be acquainted with different concepts associated with measures of central tendency and dispersion like mean median and mode Graphic representation of frequency distribution is also given We will also study about measure of variation range IQR quartile decile and percentiles Unit II This unit will make you enable to acquire the knowledge of Correlation and Regression We will study about coefficients of determination and correlation Karl Pearson s Methods Spearman s rank correlation We will also get the information of Pitfalls and limitations associated with regression and correlation analysis Unit III This unit will empower you to understand the concept of linear programming and Queuing Many business problems can be solved with the help of various linear programming methods like Simplex Methods graphical methods etc We will also get the knowledge of different queuing models related to birth death and their steady state Unit IV This unit will comprise Transportation and Assignment problems We will study about structure of transportation problem their maximization and optimality condition Assignment problem approach of the assignment model solution and maximization of assignment problem unbalanced assignment and restriction on assignment are also the content of this unit Table of Contents Third Page CONTENTS Unit No Unit Name Page Number I Measures of Central tendency and dispersion Pdf file attached II Correlation Regression Pdf file attached III Linear Programming and Queuing Pdf file attached IV Transportation and Assignment Problems Pdf file attached Glossary Key Words Mean Median Mode quartiles deciles percentiles range Karl s Pearson s coefficient Spearman s rank correlation Regression linear programming problems queuing theory transportation and assignment problems MCQ and long answer type questions last year question papers Pdf file attached References and Further Readings 1 Gupta SP Gupta PK Quantitative Techniques Operations Research Sultan Chand 2 Vohra N D Quantitative Techniques in Management McGraw Hill Education 3 Sharma J K Operations Research Problems Solutions Macmillan India Ltd 4 Render Barry Stair R M Hanna M E Badri Quantitative analysis for Management Pearson Education 1 Introduction and Learning Objectives The objective of the course is to develop student s familiarity with the basic concept and tools in statistics and operations research These techniques assist specially in resolving complex problems and serve as a valuable guide to decision makers These notes cover the entire syllabus the language is simple and notes material is self explanatory Sufficient number of illustrations of various types are given in the notes Many self assessment exercises like MCQ questions past year question papers are given in the notes Some multimedia study material like power point presentations and video lectures are also included for the better understanding of the students Syllabus E module Online Plan Video Lectures Subject Quantitative Technique Regression Analysis and Regression Equations 1 https youtu be S997LBhlqfM Linear Programming Problem 1 https youtu be ZTMTJnV67Yk 2 https youtu be L2WSzN92zhk 3 https youtu be bq4vUwaskk0 Transportation and Assignment Problem 1 https youtu be 9rB7IUvF0eg 2 https youtu be GKmLmzowbJk 3 https youtu be IwJYtYzS3Yk 4 https youtu be x7yk5GbX6RQ 5 https youtu be d P05yRNp0c 6 https youtu be jPM UTUBIHI 7 https youtu be 1lrOqmhy2VY 8 https youtu be xTylU7H4ErY 9 https youtu be Q1l JahrdSE Progress Check i Google form for self assessment MCQ based test https docs google com forms d e 1FAIpQLSeOfwIAVx26xsnQvQn3Z epWaK6Bz7miCFozT4c5Hd UtNLaVQ viewform usp sf link Essential and Additional Readings Sultan Chand Education Ltd 1 Gupta SP Gupta PK Quantitative Techniques Operations Research 2 Vohra N D Quantitative Techniques in Management McGraw Hill 3 Sharma J k Operations Research Problems Solutions Macmillan India 4 Render Barry Stair R M Hanna M E Badri Quantitative analysis for Management Pearson Education Subject Introduction to Statistics BS Mathematics Morning Evening program spring semester 2020 Chapter 03 Measures of Central Tendency Measure of Central Tendency Usually when two or more different data sets are to be compared it is necessary to condense the data but for comparison the condensation of data set into a frequency distribution and visual presentation are not enough It is then necessary to summarize the data set in a single value Such a value usually somewhere in the center and represent the entire data set and hence it is called measure of central tendency or averages Since a measure of central tendency i e an average indicates the location or the general position of the distribution on the X axis therefore it is also known as a measure of location or position Types of Measure of Central Tendency 1 Arithmetic Mean 2 Geometric Mean 3 Harmonic Mean 4 Mode 5 Median Arithmetic Mean or Simply Mean A value obtained by dividing the sum of all the observations by the number of observation is called arithmetic Mean Mean Sum of All observation Number of observation Numerical Example Calculate the arithmetic mean for the following the marks obtained by 9 students are given below Using formula of arithmetic mean for ungrouped data n xi x i 1 n n 9 x 40 marks 360 9 xi 45 32 37 46 39 36 41 48 36 n xi 360 i 1 Numerical Example Calculate the arithmetic mean for the following data given below Using formula of direct method of arithmetic mean for grouped data n fi xi x i 1 n n n fi i 1 fi i 1 106 107 111 92 76 86 84 The weight recorded to the nearest grams of 60 apples picked out at random from a consignment are given below 82 109 107 115 93 187 95 123 125 70 126 68 130 129 139 119 115 128 100
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