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: Meaning of Diagrammatic Presentation, Difference between Diagrams and Graphs, General rules for constructing Diagrams, Types of Bar Diagrams, Percentage Bar Diagrams, Deviation bar diagrams, Multiple bar diagrams, Simple bar diagram, SL Examples, Solution of Practical Questions 30 min
  • 02: Define Pie Diagrams, Draw Pie Diagrams, Graphs, 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: Basic Concepts, Mathematical Averages, Arithmetic mean, Geometric mean, Harmonic mean, SL Examples of Individual series, Discrete series, continuous series, Method of Calculation Averages, Direct Method, Indirect Method, Assume mean method, Step Deviation method, Simple Arithmetic mean, Weighted Arithmetic mean, SL Examples of Arithmetic mean, Solution of Practical Questions 50 min
  • 02: Positional Averages, Mode, Median, Formula of Arithmetic mean by Direct method, Important Formula Discuss, SL Examples, Solution of Practical Questions 48 min
  • 03: Quartiles, Deciles, Percentiles, Graphic Determination, Table of Formula of Mean, Calculation of combined mean, SL Examples, Weighted Arithmetic mean, Application to find Average speed, SL Examples on Weighted mean, Solution of Practical Questions 43 min
  • 04: Quick Revision, Correct value and Incorrect value, How to calculate Correct Mean, How to find correct mean, How to calculate correct mean If both items are consider and corrected, How to calculate correct mean If both items are ignored, SL Examples, Solution of Practical Questions 45 min
  • 05: Median, Middle value of Dispersion, Steps to find median, size of nth item, Discuss Important Formula to calculate median, How calculate C.F., Golden Concepts, SL Examples, Solution of Practical Questions 42 min
  • 06: Calculation of median when class interval are unequal, Graphic method of computing median, How to correct class-interval, How to calculate missing frequencies in Continuous series, Calculation of mode by grouping method, Discrete series, continuous series, individual series, SL Examples, Solution of Practical Questions 39 min
  • 07: Golden Concepts, Computation of Quartiles, Deciles, Percentiles, Discuss Important formula for find quartiles, deciles and Percentiles in individual, discrete and continuous series, SL Examples, Solution of Practical Questions 45 min
  • 08: Calculation of Mean in case of open-end classes, Definition of mode, Calculation of mode in Individual series, SL Examples on 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 of Geometric mean, Uses of Geometric mean, Golden Hint, How to find log, SL Examples on Log, 50 min
  • 10: Applications of Geometric mean Questions, Important on Harmonic Mean Discuss, Uses of Harmonic mean, Application on Harmonic Mean, 46 min
• Chapter 5: Measure of Variation 5 Lectures 3 hrs 35 min
  • 01: Basic Concepts, absolute and relative, Range, Quartile Deviation, Coefficient of Range, Interquartile Range, Coefficient of Quartile Deviation, Coefficient of Mean Deviation, Combined Standard Deviation, Coefficient of Variation, Dispersion Meaning, Formula for Range, SL Example on Every Topic, Formula for Coefficient of Range, Formula for Quartile Deviation, Some Important Formula Discuss, Formula for Interquartile range, Formula for Coefficient of Quartile Deviation, Quartile Deviation in Individual series Discrete series and Continuous series, Range in Individual series Discrete series and Continuous series, Solution of Practical Questions 42 min
  • 02: Mean Deviation, Standard Deviation, Variance, Mean Deviation about mean, Mean Deviation about median, Golden Concepts and Formula for Mean Deviation about mean in Individual series Discrete series and Continuous series, Golden Concepts and Formula for Mean Deviation about median in Individual series Discrete series and continuous series, Formula for Coefficient of Mean Deviation, SL Examples, Golden Concepts, Solution of Practical Questions 45 min
  • 03: Standard Deviation Concepts, Standard Deviation formula in Individual series Discrete series Continuous series, Standard Deviation formula – when deviation taken from actual mean, Standard Deviation formula – when deviation taken from assumed mean, Standard deviation formula by Direct method, SL Examples on Standard Deviation every topic, Variance formula, Combined Standard Deviation Formula, Correct or Incorrect value in Standard Deviation, Golden Rule about Standard Deviation, SL Examples, Solution of Practical Questions 38 min
  • 04: Quick Revision, Calculation of Correct mean, Calculation of Standard Deviation, Calculation of Correct Variance, Calculation of correct combined mean, SL Examples, Solution of Practical Questions 44 min
  • 05: Procedure for computing Mean Deviation, Different methods of calculating Standard Deviation, Standard Deviation computed by Short-cut method Assumed mean method and Step-deviation method, Golden Concepts in Calculation of Median, Some Important Questions, SL Examples, Solution of Practical Questions 46 min
• Chapter 6: Correlation Analysis 5 Lectures 3 hrs 35 min
  • 01: Basic Concepts, Karl Pearson’s coefficient correlation (r), Correlation Meaning, Probable Error, Rank Correlation Coefficient, Correlation Formula when Deviations are taken from actual mean, Co-variance Formula, Golden Hints, Perfect positive correlation, perfect negative correlation, Direct Method formula of Karl Pearson’s coefficient of correlation, Correlation Formula – When deviations are taken from assumed mean, SL Examples, Solution of Practical Questions 50 min
  • 02: Rank Correlation, Calculation of covariance, Computing correlation coefficient, Probable Error Formula, Formula for Rank Correlation Discuss, SL Examples on Rank Correlation, Golden Concepts, SL Examples, Solution of Practical Questions 37 min
  • 03: Golden Concepts, How to Correct Correlation, Coefficient of correlation for Bivariate Frequency Distributions, Calculation of coefficient of correlation, SL Examples, Solution of Practical Questions 44 min
  • 04: Spearman’s coefficient of rank correlation, Rank correlation – when actual ranks are given, Rank correlation – when ranks are not given, Rank correlation – when ranks are equal, SL Examples, Solution of Practical Questions 46 min
  • 05: 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 meaning, Regression equation of X on Y, Regression equation of Y on X, SL Examples, Solution on Practical Questions 50 min
  • 02: Regression Equations – Deviation taken are actual mean, Regression Equations – Deviation taken are assume mean, Calculation of bxy, Calculation of byx, Golden Hints, Correlation Coefficient, SL Examples, solution of Practical Questions 45 min
  • 03: Coefficient of correlation and two regression coefficients have the same signs, SL Examples, solution of Practical Questions 47 min
  • 04: Formula for Regression Coefficients in terms of Covariance and Variances, Formula for Regression Coefficients in terms of rank correlation and Standard Deviation, Hints to solve questions, Types of Questions in Regression Equations Discuss, SL Examples, solution of Practical Questions 42 min
  • 05: Properties of Regression Coefficients, Obtain Right regression equations from the given two regression equations, Standard Deviation of X, Standard Deviation of Y, SL Examples, solution of Practical Questions 48 min
• Chapter 8: Index Number 5 Lectures 3 hrs 41 min
  • 01: Basic Concepts, Meaning and Uses of Index Numbers, Construction of index numbers, Types of Index Numbers, Price Index Number, Quantity Index Number, Value Index Number, Methods of constructing Index Number, Simple Method formula for Index Number, weighted method for Index Number, Simple Aggregative Method, Simple average of relatives method, SL Examples, Solution of Practical questions 49 min
  • 02: Aggregative and average of relatives, Weighted Index numbers – Formula of Laspeyre’s method, Formula of Paasche’s method, Formula of Fisher’s Ideal method, Formula of Dorbish and Bowley’s method, Formula of Marshall Edgeworth method, Formula of Kelly’s method, Golden Hint for Learn Formula, Formula of Weighted Average of Relatives method, SL Examples, Solution of Practical questions 47 min
  • 03: Test of adequacy of Index numbers, Quantity Index Number, Methods of Constructing Index Number, Formula for Quantity Index Number by simple method and weighted method, Discuss Important Formula, Quick Revision of Formula, Test of consistency of Index Numbers, Time Reversal Test, Factor Reversal Test, Circular Test, Formula for Factor Reversal Test, Construction of Consumer price indices, SL Examples, Solution of Practical questions 44 min
  • 04: Construction of consumer price index, Formula for Aggregative Expenditure Method, Formula for Family Budget Method, Method of Weighted Relatives, Calculation of Cost of Living Index Number Golden Concepts, SL Examples, Solution of Practical questions 39 min
  • 05: Weighted Quantity Index Number, Formula of Weighted Average of Quantity Relatives, Chain Base Index Numbers, Base shifting, Splicing, Formula of Real wage Index Price of Living Price Index, Formula of Cost of Living Price Index, SL Examples, Solution of Practical questions 42 min
• Chapter 9: Analysis of Time Series 4 Lectures 2 hrs 58 min
  • 01: Basic Concepts, Components of time series, Analysis of time series definition, Methods of measuring trend, Freehand or graphic method, Semi-average method, moving average method, Method of least squares, SL Examples for Graphic Method, SL Examples for Semi-average method, Fit a trend line, Semi-average method when data are in even numbers, Golden Concepts for Method of moving average, Two cases for moving average – odd period moving average, even period moving average, Three yearly moving average, Four yearly moving average, SL Examples on 3 yearly moving average 48 min
  • 02: Quick Revision, SL Example for 5 yearly moving average, SL Examples for 4 yearly moving average, Additive and multiplicative models, Trend analysis, Finding trend by moving average method, SL Examples, Solution of Practical Questions 45 min
  • 03: Fitting of linear trend line using principle of least squares, Golden concepts for Methods of Least Squares, Equation of trend line, Elimination of Trend Line, SL Examples, Solution of Practical Questions 47 min
  • 04: Mathematical models for a time series, Equation of straight line trend, Methods of least squares to obtain trend values, Find Estimated no. Of units of Production, SL Examples, Solution of Practical Questions 38 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 8 Lectures 5 hrs 49 min
  • 01: Syllabus Discuss, Basic Concepts, Definition of a matrix, Rectangular array, Elements, Order of matrix, Row and column, SL example, Find order of matrix, Number of elements, Column matrix, Raw matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity or unit matrix, Zero or Null matrix, SL Examples Preview42 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 45 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 48 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 38 min
  • 05: Gold Concepts, Basic Concepts, Determinants, Some Important points, Determinant of a matrix of order one, Determinant of a matrix of order two, Determinant of a matrix of order three, Minors, Cofactors, Minor of element, Cofactors of elements of second row, Cofactors of elements of third column, SL Examples, Solution of Practical Questions 42 min
  • 06: Adjoint of a square matrix, Inverse of square matrix, SL Examples, Finding inverse of a matrix through adjoint, Transformation of Matrix, Invertible Matrices, System of Linear Equations, Steps for Matrix Inverse Method, SL Examples, Solution of Practical Questions 38 min
  • 07: Problems relating to systems of equations involving overhead allocation, Input-output model, System of Linear Equations, Methods of solving linear equations, Steps for Matrix Inverse Method, Cramer Rule Method, Determinant Method, Gauss-Jordan elimination method, SL Examples, Solution of Practical Questions 46 min
  • 08: Elementary Row operations, Inverse of a matrix by elementary operations, Gauss-Jordan elimination method, SL Examples, Solution of Practical Questions 50 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, SL Examples, Total Sales, Average Sales, How to make matrices, Solution of Practical questions 38 min
  • 02: Applications of Determinants, Consistent system, Inconsistent system, Solution of system of linear equations using inverse of a matrix, Matrix method, Homogeneous, Non-homogeneous, Discuss Golden Concepts, SL Examples, Solution of Practical Questions 46 min
  • 03: Destination Matrix, SL Examples, Total units of raw material, Golden Hints, How to solve matrix questions, Solution of Practical Questions 44 min
  • 04: Quick Revision, SL Examples, Solution of Practical Questions 35 min
  • 05: Discuss Golden Concepts, SL Examples, Solution of Practical Questions, World Problems of Linear Equations, Manufacturing Problem, Diet Problem, Investment Problem, Miscellaneous Problem 48 min
  • 06: Format of Table to solve Manufacturing Problem, At least, at most, SL Examples 43 min
  • 07: Quick revision of concepts, 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 3 Lectures 2 hrs 8 min
  • 01: Mathematical functions and their types – linear, quadratic, polynomial, Concepts of limit, Continuity of a function, Meaning of function, Use functional relationship in business and economics, domain, codomain, range, image, Constant function, linear functions, Quadratic function, Polynomial function, Rational function, 48 min
  • 02: Basic Concepts, Continuity, Dependent Variable, Independent Variable, Supply Function, Demand Function, Cost Function, Revenue Function, Profit Function, Some Important Formula Discuss, Calculate break-even values, Limit of a function, 38 min
  • 03: Limits of algebraic, exponential functions, Logarithmic functions, Continuous function, Continuity 42 min
• Chapter 4: Simple Differentiation 6 Lectures 4 hrs 11 min
  • 01: Basic Concept, Concepts of Differentiation, Rules of Differentiation, Simple Standard form, Meaning of simple differentiation, Elasticity of Demand, Some Standard Formula, some basic properties, Product Rule, Quotient Rule, Rules of Differentiation, SL Examples for Simple Differentiation Preview38 min
  • 02: Steps for Product rule apply, SL Examples for Product Rule, Solution for Practical Questions 42 min
  • 03: Quick Revision, Some Important Formula, Steps for Chain Rule apply, Solution of Practical Questions, SL Examples for Chain Rule apply 45 min
  • 04: Discuss steps for Logarithmic Differentiation apply, Some Golden Concepts, SL Examples, Solution of Practical Questions 43 min
  • 05: Exponential Functions, Implicit Function, Differentiation of Parametric Function, 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: Application of Differentiation concepts, Rate of Change, Derivative as a Rate measure, Increasing and Decreasing Function, SL Examples, SL Example on Derivative as a Rate of measure, Solution of Practical Questions 50 min
  • 02: Quick Revision, Elasticities of demand and supply, Maxima and Minima function, Define and Steps for Increasing and Decreasing Function, SL Example on Increasing decreasing function, Solution of Practical Questions 42 min
  • 03: Define Maxima and Minima of functions, Maximum value, Minimum value, Market Equilibrium, Marginal Cost, Average Cost, Steps to find Maxima and Minima, SL Example, Solution of Practical Questions 46 min
  • 04: Figure of Market Equilibrium, Involving second and third order derivatives, Relating to cost, Revenue and Profit, Marginal Revenue, Average Revenue, Marginal Revenue Product, SL Examples on Market Equilibrium, Solution of Practical Questions 38 min
  • 05: Define Marginal and cost Revenue, Important Formula, Formula of MAC, AVC, AFC, AC, Relationship between AC and MC, SL Examples, Solution of Practical questions 42 min
  • 06: Quick Revision of Concepts, SL examples, Solution of Practical Questions 40 min
  • 07: Define Marginal propensity to consume, Define Marginal propensity to save, Steps to find MPC and MPS, Define Saving Function, Define Consumption Function, SL Example, Solution of Practical Questions 39 min
  • 08: Quick Revision, Define and Discuss Elasticity of Demand and Supply, SL Examples, Solution of Practical questions 45 min
  • 09: Cost Revenue, Profit Application Define, SL Examples, Solution of Practical questions 41 min
  • 10: Price Elasticity of Demand, Maximization of Total Revenue, Minimisation of Average Cost, Solution of Practical questions 50 min
• Chapter 6: Integration and Application 10 Lectures 7 hrs 3 min
  • 01: Basic Concepts, Introduction, Application of Integration, Discuss integration by figure, Definite integral, Indefinite Integral, Integration Important formula, Golden Concepts, Integration by parts, SL Examples, Solution of Practical Questions Preview50 min
  • 02: Methods of Integration, Steps to solve Integration by parts, Integration by substitution, Integration by using partial function, SL Examples, Solution of Practical Questions 45 min
  • 03: Some Golden Concepts, Important Formula Discuss, Some Standard Results, SL Examples, Rational Function, Partial Function, Discuss Steps to solve integration by partial function, Golden Hints, SL Examples, Solution of Practical questions 41 min
  • 04: Quick Revision of Formula, 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 for Cost Function, Solution of Practical questions 42 min
  • 06: Discuss Steps For finding Average Cost Function, Steps discuss to find Revenue Function and Demand Function, SL Examples, Solution of Practical questions 49 min
  • 07: Discuss Steps For finding Revenue Function and Demand Function, SL Examples, Solution of Practical questions 38 min
  • 08: Discuss Steps For finding Maximum profit of MC and MR Functions given, SL Examples, Solution of Practical questions 41 min
  • 09: Discuss Steps For finding Consumption and Saving function when MPC and MPS are given, SL Examples, Solution of Practical questions 40 min
  • 10: Discuss Steps For finding demand function when elasticity of demand is given, Consumer Surplus, Producer’s Surplus, SL Examples, Solution of Practical questions 39 min
• Chapter 7: Mathematics of Finance 8 Lectures 5 hrs 50 min
  • 01: Basic Concepts, Introduction, Simple and compound interest, Mathematics of Finance, Future Value, Present value, Simple Interest, rate of interest, Hints to solve questions, SL Examples, Solution of Practical Questions 50 min
  • 02: Discuss Golden Steps, Formula of Compound Interest, Calculation of Amount Formula, Discuss Compounding Factor, Compounding Annually, Compounding Monthly, Compounded semi-annually, Calculate amount at the end of the year, Rate of interest – nominal, effective and continuous and their inter-relationships, SL Examples, Solution of Practical Questions 40 min
  • 03: Compounding and discounting of a sum using different types of rates, Tips for questions solve, Golden Hints, Formula of Simple Interest, SL Examples, 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, Depreciation, If depreciation charges on DBM, If depreciation charges on SLM, SL Examples, 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