Module Code and Title:       MAT203          Statistical Methods and Quantitative Techniques

Programme:                          BCA

Credit Value:                         12

Module Tutor:                       Somnath Chaudhuri

General Objective: This module aims to introduce students to the basic concepts of statistics that are necessary for higher-level quantitative reasoning skills such as the ability to analyse problems and draw valid inferences and make meaningful decisions. This includes techniques of data collection and its compilation, the calculation of various measures, and their interpretation. Linear programming is also included to emphasize the importance of thinking about how to achieve outcomes in the most optimized way. All units in the subject matter will have equivalent time devoted between theory lectures and practical exercises.

Learning Outcomes – On completion of the module, learners will be able to:

1. Collect relevant data for an intended purpose, then tabulate and prepare an appropriate chart to represent the data.
2. Calculate various measures of data like measures of central tendency, measure of variation, correlation etc., and interpret their meaning.
3. Make useful forecasts and plans using statistical reasoning.
4. Set null and alternative hypotheses and decide on their acceptability based on a test statistic.
5. Apply general as well as specially structured linear programming models in formulating decision situations to find optimal solutions.
6. Find optimal solutions for problems that pertain to job scheduling and inventory management.
7. Use a data analysis tool pack for computational data analysis.

Learning and Teaching Approach:

Assessment Approach:

A. Individual Assignment: Portion of Final Mark: 10%

Students should submit two assignments related to data collection and probability to obtain this 10%. The first one will be before the midterm and it constitutes half of the total 10% allocated. They will be submitting an assignment based on data collection and presentation. The next assignment that is for the other half will be done after the midterm, which will be on probability distributions, transportation and assignment problems. 3-4 numerical problems will be assigned to them to solve. 40% will be awarded for solving the problem, 40% for analysing the problem and 20% for the overall report.

Activity: Different problems will be assigned to the students. Students have to analyse those and solve them. Solutions should be submitted in hardcopy format with proper logical expressions.

B. Class Test: Portion of Final Mark: 20%

This is a written test conducted within the class for duration of 30-40 minutes. There will two such tests, one before midterm comprising of topics from the beginning to the quarter point of the subject matter and the other after the midterm comprising of topics from after the midterm to quarter pointer after midterm. Topics will be on central tendency, time series analysis and linear programming. Each class test will consist of 3-4 problems both theoretical and numerical. The students have to solve those problems in the class within predefined time.

Activity: In-class individual problem solving.

C. Individual Presentation: Portion of Final Mark: 5%

The presentation will be conducted within the class hours. Students are expected present the topic assigned to them respectively. The presentation will be approximately 10-12 minutes, and include power points slides. 30% will be awarded for content of the presentation, 30% for preparedness, 10% for timing, 15% for handling of Q&A session and 15% for presentation skill.

D. Lab Practical Exam: Portion of Final Mark: 20%

This component assesses the student’s practical knowledge. They will be assessed on how they can apply statistical tools for data analysis. There will be one hour practical examination. 2-3 problems will be assigned to individual student. They have to solve it within predefined examination duration. 35% will be awarded sub tasks completed, 35% Techniques used for each sub task, 10% for timing and 30% for output.

Activity: Practical problem solving in the lab.

E. Midterm Exam: Portion of Final Mark: 20%

This a college wide examination conducted at the half-way into the semester. This examination is conducted for 1 hour and 30 Minutes and it includes all topics till the half-way point in the subject matter.

Prerequisites: MAT101

Subject Matter:

1. Introduction to Statistics
   • Definition and scope of Statistics
   • Types of sampling and data collection
2. Data Collection and Presentation
   • Classification and tabulation
   • Frequency distributions
   • Charts
   • Graphical representation
3. Measures of Central Tendency and Measures of dispersion
   • Measures of central tendency and partition values
   • Measures of dispersion
   • Moments and measures of skewness and Kurtosis
4. Correlation and regression
   • Bi-variate data and scatter diagram
   • Principle of least square and curve fitting
   • Correlation and regression
   • Partial and multiple correlation coefficients
5. Time series Analysis
   • Time series data
   • Trend and seasonal variations
   • Forecast
6. Theory of probability
   • Classical, empirical and axiomatic approaches to probability
   • Addition and Multiplication theorems on probability (without proof)
   • Conditional probability and Bayes’ formula
7. Probability distributions
   • Binomial distributions
   • Poisson distributions
   • Normal distributions
8. Linear Programming, Transportation and Assignment Models
   • Two variables LP Model - Formulation and Graphical LP solution
   • Selected demonstrative LP applications in business
   • Transition from graphic to algebraic solution
   • Simplex method, Duality and Sensitivity Analysis
   • Transportation Model and its variants
   • Definition of Transportation Model
   • Assignment model as a variant of transportation model

Reading List:

1. Essential Reading
   • Richard I. Levin, David S. Rubin, (2007), Statistics for Management, 7th Edition – 4th impression, Pearson Education
   • Gupta, S.C., (2003), Fundamentals of Statistics, S. Chand Publishing Company, New Delhi
   • Gupta, S. (2012). Statistical Methods. Sultan Chand & Sons.
   • Medhi, J. (2009). Statistical Methods: An Introductory Text.
2. Additional Reading
   • Loomba, N.P. Management: A Quantitative Perspective, Macmillan.
   • Kenny,J.F. & Keeping, E.S. (1974). Mathematics of Statistics, Volume 1. 3^rd Affiliated East-West Press Pvt. Ltd.
   • Mood, A. M., Graybill F. A, and Bose, D.C. (2001). Introduction to the theory of Statistics. 3^rd TMH.
   • Spiegel,M.R. (1982), Theory and problems of Probability and statistics. Schaum’s outline series
   • Gun A.M, Gupta M.K and Das Gupta B, (2002). Fundamentals of Statistics- Volume I and II. 5^th Revised Edition. World Press Pvt. Ltd.
   • Sheldon,M.R. (2007). Introduction to Probability Models. 9^th Academic Press
   • Hamdy A. T. (Na). Operations Research-An Introduction 8th Ed. Prentice Hall of India, Pvt Ltd., New Delhi
   • Levin, R.I., Rubin, D.S., Stinson, J.P. (Na). Quantitative Approaches to Management Science. West Pub. Co.

Date: May 30, 2015