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QM-R09
(PGDM-RM 2009-11 : Term-I )
Quantitative Methods
(Faculty: Prof. S. P. Singh)
QUANTITATIVE METHODS
Course Outline
Introduction
The course deals with the application of statistics and operations research in business decision making. The course will enable students to appreciate the significance of statistics and operations research for business. In statistics students will also learn how to interpret the results of statistical analysis while in operations research they will learn how to achieve objectives in business under given constraints.
Session-wise course outline
1. INTRODUCTION & DATA COLLECTION (Session 1)
1.1. Learning objectives
1.2. Key definitions used in Statistics
1.3. Population Vs Sample
1.4. Descriptive and Inferential Statistics
1.5. Collecting Data
1.6. Types of Data
1.7. Examples
2. PRESENETING DATA IN TABLES & CHARTS (Session 1)
2.1. Introduction
2.2. Bar charts and Pie Charts
2.3. Pareto Diagrams
2.4. Ordered array
2.5. Steam and Leaf Display.
2.6. Frequency distribution, Histograms and Polygons
2.7. Cumulative distribution
2.8. Contingency tables and Scatter diagrams
3. NUMERICAL DESCRIPTIVE MEASURES (Session 2)
3.1. Measuring central tendency, Variations and Shapes
3.2. Mean, Median, Mode, Geometric mean
3.3. Quartiles
3.4. Range, Inter quartiles ranges, Variance and Standard Deviations
3.5. Co-efficient of variations and Z-Scores
3.6. Symmetric and Skewed distribution
3.7. Empirical and chebyshev rule
3.8. Five number summary and box-and-whisker plot.
3.9. Covariance and Co-efficient of correlations
3.10. Pitfalls in numerical descriptive measures and ethical issues.
4. BASIC PROBABILITY (Session 3, 4)
4.1. Basic probability concepts and definitions
4.2. Conditional Probability
4.3. Various counting rules
4.4. Even, Sample event and Sample space
4.5. Contingency table and tree diagrams
4.6. Venn diagrams
4.7. Mutually Exclusive events
4.8. Collective exhaustive events
4.9. Computing joint and marginal probability
4.10. General addition rules
4.11. Examples
4.12. Statistical Independence
4.13. Multiplication rules
4.14. Baye’s theorem and examples
4.15. Counting rules (Combination and Permutations)
5. DISCRETE PROBABILITY DISTRIBUTION (Session 5, 6)
5.1. Introduction to Probability distribution
5.2. Properties of probability distribution
5.3. Computing expected values, Variance, standard deviations
5.4. Binomial and Poisson’s distribution
5.5. Random and discrete variables
5.6. Sampling methods in Binomial distribution
5.6.1. Infinite population without replacement
5.6.2. Finite population with replacement
5.7. Poisson distribution
5.7.1. Poisson distribution formula
5.7.2. Poisson distribution haracteristics
5.7.3. Using Poisson’s tables
5.8. Examples
6. NORMAL DISTRIBUTION (Session 7, 8)
6.1. Introduction to Normal Distribution (
X
)
6.2. Computing probabilities from normal distribution
6.3. Continuous probability distribution
6.4. Effect of mean, standard deviations on the shape of Normal curve
6.5. Normal distribution shape
6.6. Normal probability Density function
6.7. Standardized normal distribution (Z)
6.7.1. Transforming to standardized normal distribution
6.7.2. Standardized normal probability density function
6.7.3. Examples
6.7.4. Comparing X and Z distribution
6.8. Probability as Area under the curve
6.9. Empirical rules
6.10. Standardized normal table
6.11. Procedure for finding normal probabilities
6.11.1. Examples
6.12. Upper trial probabilities
6.13. Probability between two values
6.14. Probability in the lower trial
6.15. Evaluating and assessing probability
7. SAMPLING DISTRIBUTION (Session 9)
7.1. Introduction to Sampling distributions
7.2. Concepts of Sampling distribution
7.3. Computing probabilities to sample mean and sample proportion
7.4. Central limit theorem
7.5. Different survey sampling methods
7.6. Evaluating survey worthiness and survey errors
7.7. Examples
8. FUNDAMENTAL OF HYPOTHESIS TESTING: ONE SAMPLE TEST
(Session 10)
8.1. Basic principle of hypothesis
8.1.1. Population mean
8.1.2. Population proportion
8.1.3. Null hypothesis
8.1.4. Alternate hypothesis
8.1.5. Level of significance
8.1.6. Type –I and Type–II error
8.2. Using hypothesis testing to test a mean or proportion
8.2.1. Z-test of hypothesis for Mean (ó Known)
8.2.2. T-test of hypothesis for Mea
n (ó Unknown)
8.2.3. Steps in hypothesis testing
8.2.4. Examples
8.3. Assumption of each hypothesis testing procedure and evaluation
8.4. Avoiding pitfalls in hypothesis testing
8.5. Ethical issues involve din hypothesis testing
9. SIMPLE LINEAR REGRESSION (Session 11, 12)
9.1. Introduction to regression
9.2. Dependent and independent variables
9.2.1. Scatter diagrams
9.2.2. Correlation analysis
9.3. Using regression analysis to predict value of dependent variables
9.4. Simple linear regression model
9.5. Least square method
9.6. Regression using SOLVER
9.7. Regression coefficients (b0 and b1)
9.7.1. Interpretation of b0 co-efficient
9.7.2. Interpretation of b1 co-efficient
9.8. Slope and co-relation coefficients
9.9. Estimating mean values and predict individual values
9.10. Examples
9.11. Basic introduction to Multiple regression analysis
10. CONFIDENCE INTERVAL ESTIMATION (Session 13, 14)
10.1. Introduction
10.2. Constructing and interpreting confidence level for mean
10.3. Constructing and interpreting confidence level for proportion
10.4. Determining sample size to develop confidence level for mean
10.5. Determining sample size to develop confidence level for proportion
10.6. Confidence interval for the mean
10.6.1. When population stdn. Dev. is known
10.6.2. When population stdn. Dev. is unknown
10.7. Confidence interval for the population
10.8. Point and Interval estimates
10.9. Estimation process
10.10. General formula
10.11. Confidence level
10.12. Students t-distribution
10.13. Degree of freedom
10.14. Examples
11. STATISTICAL APPLICATION IN QUALITY AND PRODUCTIVITY MANAGEMENT (Session 15, 16)
11.1 Introduction to basic theme of quality management
11.2 Deming’s 14 points
11.2.1 Schewart-Deming cycle
11.3 Basic aspects of 6 sigma for management
11.4 Constructing various control charts
11.4.1 P-Chart
11.4.2 X bar- Chart
11.4.3 nP-chart
11.5 Using control charts for particular data type
12. LINEAR PROGRAMMING PROBLEM (Session 17)
12.1. Introduction to L.P.P, Application of Operations Research
12.2. Formulating L.P. problem
12.3. Real/ Integer variables
12.4. Objective functions and Constraints
12.5. Solution methodologies to solve L.P.P.
12.6. Some examples of L.P.P.
12.7. How SOLVER can be used to solve L.P.P.?
12.8. Introduction to graphical method.
13. SOLVING LINEAR PROGRAMMING PROBLEM (Session 18, 19)
13.1. Graphical methods to solve L.P.P. having two variables
13.2. Bounded and Unbounded region
13.3. Primal and Dual problem
13.4. Introduction to Simplex Tableau method to solve L.P.P.
13.5. Solving L.P.P. in SOLVER (MS EXCEL)
14. TRANSPORTATION/ ASSIGNMENT MODELS (Session 20)
14.1. Introduction to Assignment/ Transportation Problem
14.2. Formulating Assignment/Transportation problem
14.3. Traveling salesman problem
14.4. Hungarian method to solve Assignment problem
14.5. Solving Assignment problem in SOLVER/ LINGO
14.6. Methods to solve transportation models
14.7. Solving Transportation models in SOLVER/ LINGO
Readings:
·
Course notes
·
Statistics for Management by TN. Srivastava and Shailendra Rego by TMH publication.
·
Operatione Research by Hillier and Libermann
·
BUSINESS STATISTICS: FIRST COURSE by Levine D.M. et al., Pearson Education.
Evaluation
Assignments: 10 Marks
Class Participation: 10 Marks
Test 1: 10 Marks
Test 2: 10 Marks
Mid_Term: 30 Marks
End-Term: 30 Marks
Max. Marks:
100 Marks
Honour Policy
Out of fairness to all students, the Students Manual of Policies is taken very seriously. All students are expected to be familiar with it and are bound by its requirements. In particular, I emphasize the importance of individual student write-ups for assignments, no collaborative work during quizzes and exams, and full contribution by all students.
Created By:
Hemanta Ranjan Deo
on
05/22/2009
at
02:02 PM
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:
PGPRM - I
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