Intended Learning Outcomes
At the completion of this course student will be able to
 Identify the scale and type of the data and basic concepts of the statistics
 Define the process of a research and select appropriate data collection method in a given situation
 Identify the method of organize and present the data
 Recognize and interpret measures of central tendency, dispersion, skewness, and kurtosis
Course Content
Algebra Operation
 Introduction to Algebra
 Define variables
 Numerical expressions and algebraic expressions
 Algebraic expression using the correct order of operations
 Algebraic expression (by adding, subtracting, dividing, multiplication)
 Transform factorize algebraic form into its factors, Factorization and Fractions
Index Numbers and Logarithms
 Describe the meaning of index numbers
 Laws of index numbers and their applications
 Explain logarithms and identify the laws of logarithms
Function and Graphs
 Find the intercept and the slope of a graph
 Find the absolute maximum/ minimum of a function using the equation and the graph
 Graph linear equations
 Find X, Y, intercept and slope for given simple linear equation
Solving Equations
 Solve Formulas and Simple Linear Equations for a specific variable
 Solve quadratic equations using quadratic formulas and factors
 Solve simultaneous equations and define them in algebraic and graphical methods
Basic Calculus
 Derivative in terms of a tangent line to the graph of the function
 Limit of the function using limit laws, Derivative at a point as a limit
 Compute algebraically the derivative function using limits
 Explain basic rules of differentiation and use them to find derivatives of products and quotients
Vector and Matrix
 Define the terminology of Vector and Matrix
 Describe geometric and algebraic properties of vectors to compute vector additions, subtractions and multiplication
 Compute the determinant of a square matrix (22) by using the definition and by using the properties of determinants
 Compute the inverse of a square matrix by using the definition and by using the properties of inverse
 Illustrate the transpose of the matrix, Solve simultaneous equations using matrices (22)
Recommended Reading
 Sancheti, D. C. & Kapoor, V. K. (2009). Business Mathematics. Sultan Chand and Sons: New Delhi
 Bradely, T. & Patlon, P. (1998). Essential Mathematics for Economics and Business. Jhone Wiley publication: New York
 Freund, J. (2001). Mathematics for Statistics. Prentice Hall of India
 Strauss, M. J., Bradley, G. L. & Smith, K. J. (2002). Calculus. Prentice Hall of India

Intended Learning Outcomes
At the completion of this course student will be able to
 Identify the scale and type of the data and basic concepts of the statistics
 Define the process of a research and select appropriate data collection method in a given situation
 Identify the method of organize and present the data
 Recognize and interpret measures of central tendency, dispersion, skewness, and kurtosis
 Describe indices theory and methods
Course Content
Introduction
 Meaning and Definition of Statistics
 Importance and Scope of Statistics
 Nature of Statistics problem and examples
 Introduction to descriptive and inferential statistics
Population and Sample
 Population and Census
 Finite and infinite population
 Sample and selecting a random sample
 Difference between parameters and statistics
Classification of Data
 Purpose of classification of data
 Advantages of classification of data
 Types of classification: Primary Data and Secondary Data
 Internal and External Data
 Qualitative and Quantitative Data
 Continuous and Discrete Data and etc.
Scales of Measurement
 Nominal, Ordinal, Interval, Ratio
Survey and Experiment
 Deference between survey and experiment
 Steps to be taken to conduct a research
Data Collection Methods
 Primary Data Collection Methods
 Secondary Data Collection Methods
 Advantages and disadvantages of each data collections methods
 Define suitable data collection method in a given scenario
 Distinguish the procedure of each data collection methods
Organization of Data
 Concept of classification and tabulation
 Construct the frequency distribution
 Basic principles of tabulation
 Use of different types of data presentation methods (bar charts, pie charts, line graphs and etc.)
Frequency Distribution
 Introduction
 Cumulative and Relative frequency distribution
 Grouped and Ungrouped frequency distribution
 Graphical representation of frequency distribution : histogram, frequency polygon, Less than ogive or More Ogive, Lawrence Curve
Measures of Central Tendency
 Uses of Central Tendency Measures
 Find and interpret the various measures of central tendency (Mean, Median, Mode)
 Merits and demerits of each type of measures
Measures of Relative Location
 Find and interpret the various measures of relative location (Quartiles, Deciles, Percentiles)
Measures of Dispersion
 Importance of measuring dispersion
 Measures of dispersion (Range, Mean deviation, Quartile Range, Variance, Standard deviation)
 Distinguish absolute and relative measures of dispersion
 Merits and demerits of each type of measures
Measures of Skewness and Kurtosis
 Symmetric and asymmetric distributions
 Skewness of distributions and interpret the nature of skewness
 Kurtosis of distributions
 Evaluate and interpret the types of kurtosis
 Calculate Skewness and Kurtosis
Indices
 Construct price, quantity, and value indices (Simple Relative Indices, Simple Aggregate Indices, Aggregate Indices, Laspeyre’s Index, Paaschey’s Index, Marshell Addedge Index, Fisher’s Index)
 Practically use of indices
Recommended Reading
 ජයතිස්ස, ඩබ් ඒ (1987) මූලික සංඛ්යාන විද්යාව 1  විස්තරාත්මක සංඛ්යානය.. කර්තෘ ප්රකාශන:නුගේගොඩ
 Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
 Pillai, R.S.N. & Bagavathi. (2018). Statistics: Theory and Practice. S. Chand & Company Ltd, India
Intended Learning Outcomes
At the completion of this course student will be able to
 Explain sets theory and probability theory in decision making
 Construct calculation for the probability values of a given events
 Discuss probability distributions
Course Content
Set theory
 Introduction
 Terminology of set theory (Union, Intersection and complement)
 Venn Diagrams representing events and their probabilities
 Union and intersection of events
 Mutually exclusive events and independent events using Venn diagram.
Introduction to Probability
 Terminology of probability
 Basic rules of probability
 Random events
 Permutation and Combination
 Venn Diagrams representing events and their probabilities
 Union and intersection of events
 Mutually exclusive events and independent events
 Conditional probability of a given event
 Bayes’ Theorem
Random variables
 Identify random variables
 Discrete and continuous random variables
 Expected value and Variance of discrete random variable and continuous random variable.
Discrete Probability distribution
 Identify discrete probability distribution
 Probability mass function
 Uniform distribution
 Binomial distribution
 Poisson distribution
 Hyper geometric distribution
Continuous Probability distribution
 Identify continuous probability distribution
 Probability density function
 Uniform distribution
 Normal distribution
 Exponential distribution
Recommended Reading
 ජයතිස්ස, ඩබ් ඒ (1991). මූලික සංඛ්යාන විද්යාව 2  සම්භාවිතාව සහ ව්යාප්ති න්යාය. කර්තෘ ප්රකාශන: නුගේගොඩ
 Kandasamy, P., Thilagavathi, K. & Gunavathi, K. (2005). Probability Statistics and Queueing Theory. Chand & Company Ltd, India.
 Ross, S. (2019). A First Course in Probability. (10^{th} Edition). Pearson Education
Intended Learning Outcomes
At the completion of this course student will be able to
 Discuss basic concepts of the statistical inference procedure and various methods of point estimators and their characteristics
 Construct interval estimates, confidence intervals and confidence limit
 Explain the various concepts related to the testing of hypothesis
Course Content
Statistical Inference Procedure
 Introduction to Statistical Inference
 Type of Estimation (point estimation, interval estimation)
 Properties of a good point estimation
Point Estimation
 Population mean
 Population proportion
 Population variance and standard deviation
Interval estimation
 Confidence interval (population mean, difference between two population means, population proportion, difference between two population proportions, population variance, difference between two population variances, population standard deviation, difference between two population standard deviation)
 Determination of sample size
Hypothesis Testing
 Procedure for hypothesis testing
 Type I and II errors
 One tailed and Two tailed test
 Hypothesis test for large sample (Population Mean, Difference between two population mean, Population Proportion, Difference between two population Proportion, Population Variance, Difference between two populations variance)
 Hypothesis tests for small sample
 Paired Sample t test
Recommended Readings:
 ජයතිස්ස, ඩබ් ඒ (1991). මූලික සංඛ්යාන විද්යාව 3  අනුමිතික සංඛ්යානය. කර්තෘ ප්රකාශන: නුගේගොඩ
 Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
 Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Fry, M. J., Cochran, J. J. & Ohlmann, J. W. (2014). Statistics for Business and Economics. Cengage Learning India Private Limited:Delhi, India
Intended Learning Outcomes
At the completion of this course student will be able to
 Explain the sampling techniques in field of Social Sciences
 Discuss the Sampling methods.
 Differentiate the basic principles and methods underlying sample surveys
Course Content
Introduction to Sampling Methods
 Introduction, Terminology, Sampling Survey, Methods of Sampling
Probability Sampling Techniques
 Simple Random sampling
 Stratified random sampling
 Systematic sampling
 Cluster sampling (Introduction, Merits and Demerits, Calculations)
Nonprobability Sampling Techniques
 Quota sampling
 Convenience sampling
 Judgmental sampling
 Purposive sampling
 Snowball sampling (Introduction, merits and demerits)
Applications
 Practical applications of the sampling methods
Recommended Reading:
 ජයතිස්ස, ඩබ් ඒ (1991). මූලික සංඛ්යාන විද්යාව 3  අනුමිතික සංඛ්යානය. කර්තෘ ප්රකාශන: නුගේගොඩ
 Ardilly, P. and Tille, Y. (2006). Sampling Methods: Exercise and Solutions. Springer: Verlag, New York
 Thompson, S.K. (2002). Sampling. Wiley Series in Probability and Statistics
Intended Learning Outcomes
At the completion of this course student will be able to
 Discuss the situations where nonparametric tests are used
 Construct appropriate NonParametric Tests
Course Content
Introduction to NonParametric Tests
 Advantages and Disadvantages of NonParametric Methods, Uses of NonParametric Methods
Types of NonParametric Methods
 The Sign test for Paired data
 One Sample Sign Test
 Rank Sum Test
 MannWhitney U Test and KruskalWallis Test (H Test)
 One Sample Runs Test
 Median Test for Randomness (Runs above and below the median)
 Spearman’s Rank Correlation Test
 Testing hypothesis about Rank Correlation
 KolmogorovSmirnov Test
 Kendall Test of Concordance
 Median Test for Two Independent Samples
 Wilcoxon’s Signed Rank Test
 The matched pairs Sign Test
 ChiSquare test (Introduction, ChiSquare defined, Conditions for applying ChiSquare Test, Yate’s corrections, uses of ChiSquare test: independence, goodness of fit, homogeneity, Misuses of chisquare test, limitations of chisquare test)
Recommended Reading
 Arora, P.N., Arora, S., Arora, S. & Arora, A. (2007). Comprehensive Statistical Methods. Chand & Company Ltd: India
 Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Fry, M. J., Cochran, J. J. & Ohlmann, J. W. (2014). Statistics for Business and Economics. Cengage Learning India Private Limited:Delhi, India
 Levin, R. I., Rubin, D. S., Siddiqui, M. H. & Rastogi, S. (2017). Statistics for Management. (8^{th} Edition). Pearson India Education Service Pvt Ltd: India
Intended Learning Outcomes:
At the completion of this course student will be able to
 Clarify dependent and independent variables and the pattern of raw data.
 Calculate correlation between dependent variable and one or more independent variables.
 Compute the regression mode
 Use Statistical software to do statistical analysis
Course Content
Correlation
 Identify dependent variable and the independent variable
 Draw scatter plot
 Identify the patterns and outliers from the scatter plot
 Calculate and Interpret Correlation coefficients (Pearson correlation, Partial correlation, Spearman correlation, Correlation coefficient by Twoway tables)
 Define the merits and demerits of different types of Correlation Coefficients
 Practical applications of the correlation coefficient
Simple Linear Regression Analysis
 Introduction to Simple Linear Regression
 Assumptions of the linear regression
 Regression coefficients using OLS method
 Interpret OLS regression coefficients
 Calculate and interpret R square
 Test the significance of the parameters and the overall significance of the model
 Construct and interpret a confidence interval for the parameters
Multiple linear Regression analysis
 Describe the relationship between two or more independent variables with dependent variable
 Compute and interpret the multiple regression coefficients
 Calculate and interpret R square
 Determine the significance of regression coefficients
 Overall significance of the model
 Violation of the Assumptions of the Basic Model: Multicolinearity (Identification, Effect and Treatments)
 Autocorrelation (Identification, Effect and Treatments), Heteroscedasticity (Identification, Effect and Treatments)
Statistical software
 Use the Statistical software for data analysis
Recommended Reading
 සේමසිංහ, ඩබ්. එම්., (2015). ආර්ථිකමිතිය න්යාය හා භාවිතය. සරසවි ප්රකාශකයෝ: නුගේගොඩ
 Gujarati, D. N. (2004). Basic Econometrics. (4^{th} Edition). Tata McGrawHill Publishing Company Limited: NewDelhi, India
 Maddala, G. S. (2005). Introduction to Econometrics. (3^{rd} Edition). John Wiley & Sons Ltd. New York
 Koutsoyiannis, A. (2005). Theory of Econometrics. (2^{nd} Edition). Palgrave: New York
Intended Learning Outcomes
At the completion of this course student will be able to
 Clarify the background of Operational Research
 Compute linear programming problems in different methods
 Use Transportation problems and assignment problems in different method
 Apply methodologies for analyzing networks of different ways
Course Content
Introduction to Operational Research
 The historical development of operational research
 Operational research techniques
 Limitations of applications of operational research
 Methodology of operational research
Linear programming
 Introduction to linear programing
 Formulate linear programming problems
 General statement of linear programming problems
 Assumptions of linear programming
 Solutions using graphical method
 Special cases in graphical method (multiple optimal solutions, infeasibility and unboundedness)
 Introduction to simplex method
 Solutions using simplex methods
 BigM method, Twophase method
 Special cases in simplex method (multiple optimal solutions, infeasibility unboundedness and degeneracy problem)
 Duality in linear programming
 Dual Simplex method
 Sensitivity analysis in linear programing
Transportation Problems
 Introduction to transportation problems
 Types of transportation problems
 Finding the basic feasible solution (NorthWest corner method
 Least Cost method
 Vogel’s approximation method)
 Finding the optimal feasible solution (Stepping Stone method, Modified distribution method)
 Special cases in transportation problem (Unbalanced transportation problem
 Multiple Solutions transportation problems
 Degeneracy problem, maximization problem, restrictions of routes)
 Solutions to the transportation problems using linear programming
 Sensitivity analysis in transportation problem
Assignment Problem
 Introduction to Assignment Problem
 Hungarian Assignment method
 Solutions to the Assignment problems using linear programming
 Special cases in Assignment problem (Unbalanced Assignment problems
 Constrained Assignment problems, Multiple Optimal Solutions, Maximization Case)
Network Analysis
 Introduction Network Problems
 Critical Path Method (CPM)
 Network Analysis (Scheduling the activities, Earliest and Latest time, Determining the critical path, Calculation of Floats)
 Resource analysis and allocation (Crashing, Resource Levelling)
 Programme Evaluation and Review Technique (PERT)
 Difference between PERT and CPM
 Shortest route problem
 Maximum flow problem
 Minimum Spanning Tree Problem
Recommended Readings:
 Vohra, N. D. (2014). Quantitative Techniques in Management. (4^{th} edition). McGraw Hill Education (India) Private Limited: New Delhi
 Hira, D. S. & Guptha, P. K. (2005). Operations Research. S. Chand & Company Ltd, New Delhi