Business Mathematics and Statistics

Course Syllabus : for Business Mathematics and Statistics

Part A: Business Statistics

• Chapter 1: Introduction to Statistics 2 Lectures 1 hrs 15 min
  • 01: Meaning of Statistics, Characteristics of Statistics, Uses of Statistics 35 min
  • 02: Important functions of Statistics, Limitations of Statistics, Statistics in Business, commerce and Industry, Statistics in Economics, Statistics in Research 40 min
• Chapter 2: Classification and Tabulation 2 Lectures 1 hrs 13 min
  • 01: Meaning of Classification, Objects of classification, Types of Classifications, Geographical Classification, Chronological Classifications, Qualitative Classification, quantitative Classification, SL Examples, Solution of Practical Questions 35 min
  • 02: Discrete Frequency Distributions, Continuous Frequency Distributions, Discrete series, continuous series, Individual series, Class Interval, Table Making, SL Examples, Solution of Practical Questions 38 min
• Chapter 3: Diagrammatic and Graphic Representation 2 Lectures 1 hrs 9 min
  • 01: Difference between Diagrams and Graphs, Types of Bar Diagrams - Percentage Bar Diagrams, Deviation bar diagrams, Multiple bar diagrams, Simple bar diagram, SL Examples 30 min
  • 02: Pie Diagrams, Technique to constructing Graphs, Graph of one variable, Graph of two variable, SL Examples, Solution of Practical Questions 39 min
• Chapter 4: Measure of Central Tendency 10 Lectures 7 hrs 36 min
  • 01: Mathematical Averages, Arithmetic mean, Geometric mean, Harmonic mean, Method of Calculation of Averages - Direct Method, Indirect Method, SL Examples 50 min
  • 02: Positional Averages, Mode, Median, Arithmetic mean by Direct method, Important Formula, SL Examples, Solution of Practical Questions 48 min
  • 03: Quartiles, Deciles, Percentiles, Calculation of combined mean, SL Examples, Weighted Arithmetic mean, Application to find Average speed, SL Examples 43 min
  • 04: Assume mean method, Step Deviation method, Correct value and Incorrect value, Calculate Correct Mean, Solution of Practical Questions 45 min
  • 05: Steps to find median, size of nth item, Important Formula, How calculate C.F., Golden Concepts, Solution of Practical Questions 42 min
  • 06: Calculation of median, Graphic method of computing median, How to correct class-interval, Calculate missing frequencies, Calculation of mode by grouping method, SL Examples 39 min
  • 07: In Individual, Discrete and Continuous series - Computation of Quartiles, Deciles, Percentiles, Important formula, Solution of Practical Questions 45 min
  • 08: Calculation of mode, Analysis Table to find mode, Grouping Table to find mode, SL Examples, Solution of Practical Questions 48 min
  • 09: Graphic method of locating mode, Important Formula, Uses of Geometric mean, Golden Hint, How to find log, SL Examples on Log 50 min
  • 10: Applications of Geometric mean, Calculation of Harmonic Mean, Application on Harmonic Mean, Solution of Practical Questions 46 min
• Chapter 5: Measure of Variation 5 Lectures 3 hrs 35 min
  • 01: Range, Quartile Deviation, Coefficient of Range, Interquartile Range, Coefficient of Quartile Deviation, Combined Standard Deviation, Coefficient of Variation, Solution of Practical Questions 42 min
  • 02: Mean Deviation, Standard Deviation, Variance, Mean Deviation about mean, Mean Deviation about median, Coefficient of Mean Deviation, SL Examples 45 min
  • 03: Standard Deviation formula – when deviation taken from actual mean, and when deviation taken from assumed mean, Variance formula, Solution of Practical Questions 38 min
  • 04: Calculation of Correct mean, Calculation of Correct Standard Deviation, Calculation of Correct Variance, Calculation of correct combined mean, SL Examples 44 min
  • 05: Standard Deviation computed by Short-cut method, Assumed mean method and Step-deviation method, Solution of Practical Questions 46 min
• Chapter 6: Correlation Analysis 5 Lectures 3 hrs 35 min
  • 01: Karl Pearson’s coefficient correlation (r), Rank Correlation Coefficient, Perfect positive correlation, perfect negative correlation, SL Examples 50 min
  • 02: Formula for Rank Correlation, Calculation of covariance, Computing Correlation Coefficient, Probable Error Formula, SL Examples 37 min
  • 03: Calculate Correct Correlation, Coefficient of correlation for Bivariate Frequency Distributions, Calculation of coefficient of correlation, Solution of Practical Questions 44 min
  • 04: Spearman’s coefficient of rank correlation, Rank correlation – when actual ranks are given, SL Examples, Solution of Practical Questions 46 min
  • 05: Rank correlation – when ranks are not given, Rank correlation – when ranks are equal, SL Examples, Solution of Practical Questions 38 min
• Chapter 7: Regression Analysis 5 Lectures 3 hrs 52 min
  • 01: Linear regression Analysis, Regression equations, Least squares approach, Regression equation of X on Y, Regression equation of Y on X, SL Examples 50 min
  • 02: Regression Equations – Deviation taken are actual mean, Regression Equations – Deviation taken are assume mean, Calculation of bxy, Calculation of byx, SL Examples 45 min
  • 03: Coefficient of correlation, Formula for Regression Coefficients in terms of Covariance and Variances, Golden Hints, solution of Practical Questions 47 min
  • 04: Formula for Regression Coefficients in terms of rank correlation and Standard Deviation, solution of Practical Questions 42 min
  • 05: Properties of Regression Coefficients, Obtain Right regression equations from the given two regression equations, Solution of Practical Questions 48 min
• Chapter 8: Index Number 7 Lectures 5 hrs 13 min
  • 01: Construction of Index numbers, Price Index Number, Simple Method and Weighted Method, Simple Aggregative Method, Solution of Practical questions 49 min
  • 02: Weighted Index numbers – Lapser’s method, Paasche’s method, Fisher’s Ideal method, Weighted Average of Relatives method, SL Examples 47 min
  • 03: Weighted Index numbers – Dorbish and Bowler’s method, Marshall Edge worth method, Kelly’s method, Golden Hint for Learn Formula, SL Examples 44 min
  • 04: Test of adequacy of Index numbers, Methods of Constructing Index Number, Formula for Quantity Index Number, Solution of Practical questions 39 min
  • 05: Construction of consumer price index, Aggregative Expenditure Method, Family Budget Method, Calculation of Cost of Living Index Number, Solution of Practical questions 42 min
  • 06: Test of consistency of Index Numbers, Time Reversal Test, Circular Test, Formula for Factor Reversal Test, Construction of Consumer price indices, SL Examples 45 min
  • 07: Weighted Quantity Index Number, Chain Base Index Numbers, Base shifting, Splicing, Cost of Living Price Index, Solution of Practical questions 47 min
• Chapter 9: Analysis of Time Series 5 Lectures 3 hrs 47 min
  • 01: Time Series, Methods of measuring Trend, Freehand or graphic method, Semi-average method, Moving average method, Method of least squares, SL Examples 48 min
  • 02: Fit a trend line, Semi-average method when data are in even numbers, Two cases for moving average – odd and even period moving average, SL Examples 45 min
  • 03: SL Example for 5 yearly moving average, Trend analysis, Finding trend by moving average method, Solution of Practical Questions 47 min
  • 04: Fitting of linear trend line using principle of least squares, Golden Concepts, Equation of trend line, Elimination of Trend Line, Solution of Practical Questions 38 min
  • 05: Mathematical models for a time series, Equation of straight line trend, Methods of least squares to obtain trend values, Solution of Practical Questions 49 min
• Chapter 10: Interpretation of Data 1 Lectures 35 min
  • 01: Data are homogeneous – they are strictly comparable, Data are collected without bias, Inconsistency in Definition, Misuse of Various Tools of Analysis like Mean, median, mode, Dispersion, Correlation, Failure to comprehend the total background of the Data 35 min

Part B: Business Mathematics

• Chapter 1: Matrices and Determinants 9 Lectures 6 hrs 28 min
  • 01: Order of matrix, Number of elements, Column matrix, Raw matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, Zero or Null matrix, SL Examples Preview47 min
  • 02: Types of matrices, Algebra (Operation) of Matrices, Addition of Matrices, Scalar multiplication, Multiplication of Matrices, Subtraction of Matrices, SL Examples, Solution of Practical Questions 42 min
  • 03: Algebra of matrices, Equality of Matrices, Negative of Matrix, Difference of Matrices, Properties of Matrix Addition, multiplication of matrices, Scalar Matrix, Scalar multiplication, Subtraction of Matrices, SL Examples, Solution of Practical Questions 37 min
  • 04: Calculation of values of determinants up to third order, Transpose of a Matrix, Symmetric and Skew Symmetric Matrices, SL Examples, Solution of Practical Questions 39 min
  • 05: Determinant of a matrix of order one, Determinant of a matrix of order two, Determinant of a matrix of order three, Solution of Practical Questions 45 min
  • 06: Minors, Cofactors, Adjoin of a square matrix, Inverse of square matrix, Finding inverse of a matrix through adjoin, Solution of Practical Questions 37 min
  • 07: Transformation of Matrix, Invertible Matrices, System of Linear Equations, Steps for Matrix Inverse Method, Solution of Practical Questions 48 min
  • 08: System of Linear Equations, Methods of solving linear equations, Cramer Rule Method, Determinant Method, Solution of Practical Questions 51 min
  • 09: Elementary Row operations, Inverse of a matrix by elementary operations, Gauss-Jordan elimination method, Solution of Practical Questions 42 min
• Chapter 2: Application of Matrices and Determinants 8 Lectures 5 hrs 44 min
  • 01: Application of matrices for solution to simple business and economic problems, Tips to solve questions, How to make matrices, Matrix method, SL Examples 38 min
  • 02: Consistent system, Inconsistent system, Solution of system of linear equations using inverse of a matrix, Golden Concepts, Solution of Practical Questions 46 min
  • 03: Destination Matrix, SL Examples, Golden Hints, How to solve matrix questions, Solution of Practical Questions 44 min
  • 04: Applications of Determinants, SL Examples, Solution of Practical Questions 35 min
  • 05: Solution of Practical Questions, World Problems of Linear Equations, Manufacturing Problem, Solution of Practical Questions 48 min
  • 06: Format of Table to solve Manufacturing Problem, At least, at most, SL Examples, Solution of Practical Questions 43 min
  • 07: Diet Problem, Investment Problem, Miscellaneous Problem, Solution of given inequation, Solution of Practical Questions 41 min
  • 08: SL Examples, Solution of Practical Questions 49 min
• Chapter 3: Functions, Limits and Continuity 4 Lectures 2 hrs 55 min
  • 01: Linear, Quadratic, Polynomial, Limit, Continuity of a function, Domain, Co-domain, range, image, Constant function, linear functions, SL Examples 48 min
  • 02: Dependent Variable, Independent Variable, Supply Function, Demand Function, Cost Function, Revenue Function, SL Examples 38 min
  • 03: Profit Function, Important Formula, Calculate break-even values, Limit of a function, Quadratic function, Polynomial function, SL Examples 42 min
  • 04: Limits of algebraic, exponential functions, Logarithmic functions, Continuous function, Rational function, SL Examples 47 min
• Chapter 4: Simple Differentiation 6 Lectures 4 hrs 11 min
  • 01: Differentiation, Rules of Differentiation, Simple Standard form, Elasticity of Demand, Rules of Differentiation, SL Examples Preview38 min
  • 02: Product Rule, Quotient Rule, Steps for Product rule, SL Examples, Solution for Practical Questions 42 min
  • 03: Differentiation of Parametric Function, Important Formula, Steps for Chain Rule, Solution of Practical Questions 45 min
  • 04: Steps for Logarithmic Differentiation, Exponential Functions, Implicit Function, Golden Concepts, Solution of Practical Questions 43 min
  • 05: Higher Order Derivative, First Order Derivative, Second Order Derivative, SL Examples, Solution of Practical Questions 38 min
  • 06: Derivative of the inverse of a function, Successive differentiation, Third derivative, SL Examples, Solution of Practical Questions 45 min
• Chapter 5: Application of Differentiation 10 Lectures 7 hrs 13 min
  • 01: Rate of Change, Derivative as a Rate measure, Increasing and Decreasing Function, SL Examples, SL Example, Solution of Practical Questions 50 min
  • 02: Elasticity of demand and supply, Maxima and Minima function, Steps for Increasing and Decreasing Function, Solution of Practical Questions 42 min
  • 03: Maxima and Minima of functions, Maximum value, Minimum value, Steps to find Maxima and Minima, SL Example, Solution of Practical Questions 46 min
  • 04: Revenue and Profit, Marginal Revenue, Average Revenue, Marginal Revenue Product, SL Examples, Solution of Practical Questions 38 min
  • 05: Marginal and Cost Revenue, Formula of MAC, AVC, AFC, AC, Relationship between AC and MC, Solution of Practical questions 42 min
  • 06: Market Equilibrium, Marginal Cost, Average Cost, SL examples, Solution of Practical Questions 40 min
  • 07: Marginal propensity to consume, Marginal propensity to save, Steps to find MPC and MPS, Saving Function, Consumption Function, SL Example 39 min
  • 08: Elasticity of Demand and Supply, SL Examples, Solution of Practical questions 45 min
  • 09: Average Cost, Cost Revenue, Profit Application Define, SL Examples, Solution of Practical questions 41 min
  • 10: Price Elasticity of Demand, Maximization of Total Revenue, Minimisation of Solution of Practical questions 50 min
• Chapter 6: Integration and Application 10 Lectures 7 hrs 2 min
  • 01: Application of Integration, Definite integral, Indefinite Integral, Integration Important formula, Golden Concepts, Integration by parts, SL Examples Preview49 min
  • 02: Steps to solve Integration by parts, Integration by substitution, Integration by using partial function, Golden Hints, Solution of Practical Questions 45 min
  • 03: Important Formula, Some Standard Results, SL Examples, Rational Function, Steps to solve integration by partial function, Solution of Practical questions 41 min
  • 04: Upper Limit, Lower Limit, Steps to solve Integration of limit, SL Examples, Solution of Practical questions 38 min
  • 05: Application of Integration in Business and Economics, For finding Cost Function, SL Example, Solution of Practical questions 42 min
  • 06: Steps For finding Average Cost Function, Steps to find Revenue Function and Demand Function, SL Examples, Solution of Practical questions 49 min
  • 07: Steps For finding Revenue Function and Demand Function, SL Examples, Producer’s Surplus, Solution of Practical questions 38 min
  • 08: Steps For finding Maximum profit of MC and MR Functions given, SL Examples, Solution of Practical questions 41 min
  • 09: Steps For finding Consumption and Saving function when MPC and MPS are given, Consumer Surplus, SL Examples, Solution of Practical questions 40 min
  • 10: Steps For finding demand function when elasticity of demand is given, SL Examples, Solution of Practical questions 39 min
• Chapter 7: Mathematics of Finance 8 Lectures 5 hrs 50 min
  • 01: Simple interest, Compound Interest, Future Value, Present value, Simple Interest, rate of interest, Hints to solve questions, SL Examples 50 min
  • 02: Compounding Factor, Compounding Annually, Compounded semi-annually, Rate of interest – nominal, effective and continuous, Solution of Practical Questions 40 min
  • 03: Compounding and discounting of a sum using different types of rates, Golden Hints, Solution of Practical Questions 46 min
  • 04: Continuous compounding of interest, Important formula, Compounding continuously, Effective Rate of Interest, Compounding normal rate, Compounding effective rate, Formula of Effective rate discuss, SL Examples, Solution of Practical Questions 42 min
  • 05: Present value at discount rate, Effective rate of discount, If depreciation charges on DBM, If depreciation charges on SLM, Solution of Practical Questions 48 min
  • 06: How to find Log and Antilog, Convert into antilog, Formula for Compound Amount, Golden Concepts, SL Examples, Solution of Practical Questions 35 min
  • 07: Compound amount at changing rates, Formula of Present Value, Discount, SL Examples, Solution of Practical Questions 41 min
  • 08: Methods of computing the annual depreciation, Compound Interest Formula, SL Examples, Solution of Practical Questions 48 min