Business Mathematics and Statistics

Cover
Contents
1. Introduction: Scope, Data Collection and Classification
	1.1 Meaning of ‘Statistics’
	1.2 Variable and Attribute
	1.3 Primary Data and Secondary Data
	1.4 Population (or Universe) and Sample
	1.5 Complete Enumeration (or Census) and Sample Survey
	1.6 Statistical Enquiry
	1.7 Useful Terms
	1.8 Classification
	1.9 Tabulation
	1.10 Mechanical Tabulation
	1.11 Additional Example
	Exercises
	Answers
2. Permutation
	2.1 Introduction
	2.2 Fundamental Rules of Counting
	2.3 Results on Permutation
	2.4 Additional Examples
	Exercises
	Answers
3. Combination
	3.1 Introduction
	3.2 Results of Combination
	3.3 Additional Examples
	Exercises
	Answers
4. Set Theory
	4.1 Set
	4.2 Methods of Set Representation and Notation
	4.3 Types of Sets
	4.4 Venn Diagram
	4.5 Set Operations
	4.6 Union (Set Addition)
	4.7 Intersection (Set Multiplication)
	4.8 Complement
	4.9 Difference
	4.10 Examples on Set Operations
	4.11 Laws of Algebra of Sets
	4.12 Duality
	4.13 Verification of Laws (Using Venn Diagram)
	4.14 Proof of the Laws of Set Algebra
	4.15 Number of Elements in a Set
	4.16 Additional Examples
	Exercises
	Answers
5. Logarithm
	5.1 Introduction
	5.2 Definition of Logarithm
	5.3 Laws of Logarithm
	5.4 Additional Examples
	5.5 Common Logarithm and Natural Logarithm
	5.6 Antilogarithm
	Exercises
	Answers
6. Binomial Theorem
	6.1 Introduction
	6.2 Binomial Theorem
	6.3 General Term of (a + x)n
	6.4 Middle Term(s) of (a + x)n
	6.5 Equidistant Terms and Coefficients
	6.6 Greatest Binomial Coefficient(s)
	6.7 Properties of Binomial Coefficient(s)
	6.8 Additional Examples
	Exercises
	Answers
7. Compound Interest
	7.1 Introduction
	7.2 Definition of Important Terms
	7.3 Simple Interest
	7.4 Compound Interest
	7.5 Interest Compounded Continuously
	7.6 Amount at the Changing Rates of Interest
	7.7 Nominal and Effective Rate of Interest
	7.8 Growth and Depreciation
	7.9 Additional Examples
	Exercises
	Answers
8. Annuities
	8.1 Introduction
	8.2 Amount of Immediate Annuity or Ordinary Annuity
	8.3 Present Value of Immediate Annuity or Ordinary Annuity
	8.4 Amount of Annuity Due
	8.5 Present Value of Annuity Due
	8.6 Amount of a Deferred Annuity
	8.7 Present Value of a Deferred Annuity
	8.8 Perpetual Annuity or Perpetuity
	8.9 Amortisation
	8.10 Sinking Fund
	8.11 Additional Examples
	Exercises
	Answers
9. Other Useful Mathematical Devices
	9.1 Rounding of Numbers
	9.2 Absolute, Relative and Percentage Errors
	9.3 Significant Figures
	9.4 Some Short Processes of Calculation
	9.5 Roots and Reciprocals Expressed as Power
	9.6 A.P. Series and G.P. Series
	9.7 Sum and Sum of the Squares of Numbers
	9.8 Inequalities
	9.9 Concept of ‘Function’
	9.10 Polynomial
	9.11 Sigma (S) Notation
	9.12 Simple Interpolation
10. Charts and Diagrams
	10.1 Objects of Diagrammatic Representation
	10.2 Types of Charts and Diagrams
	10.3 Additional Examples
	Exercises
	Answers
11. Frequency Distribution
	11.1 Observation, Frequency
	11.2 Simple Series (or Ungrouped Data) and Frequency Distribution
	11.3 Useful Terms Associated with Grouped Frequency Distributions
	11.4 Construction of Frequency Distribution
	11.5 Cumulative Frequency Distribution
	11.6 Relative Frequency Distribution
	11.7 Diagrammatic Representation of Frequency Distributions
	11.8 Frequency Curve
	11.9 Additional Examples
	Exercises
	Answers
12. Measures of Central Tendency
	12.1 Averages or Measures of Central Tendency
	12.2 Arithmetic Mean (A.M.)
	12.3 Important Properties of A.M.
	12.4 Simplified Calculation for A.M.
	12.5 Mean of Composite Group
	12.6 Geometric Mean (G.M.)
	12.7 Properties of G.M.
	12.8 Harmonic Mean (H.M.)
	12.9 Advantages and Disadvantages of A.M., G.M., H.M.
	12.10 Relations between A.M., G.M., H.M.
	12.11 Median
	12.12 Calculation of Median
	12.13 Advantages and Disadvantages of Median
	12.14 Mode
	12.15 Calculation of Mode
	12.16 Advantages and Disadvantages of Mode
	12.17 Relation between Mean, Median, Mode
	12.18 Partition Values—Quartiles, Deciles, Percentiles
	12.19 Calculation of Partition Values
	12.20 Additional Examples
	Exercises
	Answers
13. Measures of Dispersion
	13.1 Meaning and Necessity of ‘Measures of Dispersion’
	13.2 Range
	13.3 Quartile Deviation (or Semi-interquartile Range)
	13.4 Mean Deviation (or Mean Absolute Deviation)
	13.5 Standard Deviation (S.D.)
	13.6 Important Properties of S.D.
	13.7 Calculation of Standard Deviation (s)
	13.8 S.D. of Composite Group
	13.9 Relation between S.D. and Other Measures
	13.10 Relative Measures of Dispersion
	13.11 Additional Examples
	Exercises
	Answers
14. Moments, Skewness and Kurtosis
	14.1 Moments
	14.2 Relation between Central and Non-central Moments
	14.3 Beta-coefficients and Gamma-coefficients
	14.4 Standardized Variable
	14.5 Moments of Frequency Distributions
	14.6 Skewness
	14.7 Kurtosis
	14.8 Additional Examples
	Exercises
	Answers
15. Curve Fitting
	15.1 Curve Fitting
	15.2 Straight Line and Parabola
	15.3 Free-hand Method of Curve Fitting
	15.4 Method of Least Squares
	15.5 Fitting Straight Line
	15.6 Simplified Calculations
	15.7 Fitting Parabola
	15.8 Fitting Exponential and Geometric Curves
	Exercises
	Answers
16. Correlation and Regression
	16.1 Concepts of ‘Correlation’ and ‘Regression’
	16.2 Bivariate Data
	16.3 Bivariate Frequency Distribution
	16.4 Scatter Diagram
	16.5 Correlation
	16.6 Covariance
	16.7 Correlation Coefficient (r)
	16.8 Properties of Correlation Coefficient
	16.9 Calculation of r
	16.10 Interpretation and Use of r
	16.11 Variance of the Sum (Difference) of Two Series
	16.12 Regression
	16.13 Properties of Linear Regression
	16.14 Explained Variation and Unexplained Variation
	16.15 Regression Curve in Bivariate Frequency Distribution
	16.16 Rank Correlation
	16.17 Additional Examples
	Exercises
	Answers
17. Association of Attributes
	17.1 Introduction
	17.2 Notations and Data Classification
	17.3 Contingency Table
	17.4 Type of Association
	17.5 Measures of Association
	Exercises
	Answers
18. Interpolation
	18.1 Introduction
	18.2 Finite Differences: D and E Operators
	18.3 Differences of a Polynomial Function
	18.4 Newton’s Forward Interpolation Formula
	18.5 Newton’s Backward Interpolation Formula
	18.6 Lagrange’s Interpolation Formula
	18.7 Inverse Interpolation
	18.8 Additional Examples
	Exercises
	Answers
19. Index Numbers
	19.1 Meaning of ‘Index Number’
	19.2 Problems in Construction of Index Numbers
	19.3 Methods of Construction of Index Numbers
	19.4 Quantity Index Number
	19.5 Tests of Index Numbers
	19.6 Chain Base Method
	19.7 Cost of Living Index Numbers
	19.8 Bias in Laspeyres’ and Paasche’s Formulae for C.L.I.
	19.9 Base Shifting, Splicing and Deflation
	19.10 Errors in Index Numbers
	19.11 Additional Examples
	Exercises
	Answers
20. Time Series
	20.1 Meaning and Necessity of ‘Time Series Analysis’
	20.2 Components of Time Series
	20.3 Adjustments to Time Series Data
	20.4 Secular Trend
	20.5 Measurement of Trend
	20.6 Monthly Trend from Annual Data
	20.7 Seasonal Variation
	20.8 Measurement of Seasonal Variation
	20.9 Cyclical Fluctuation
	20.10 Business Forecasting
	20.11 Exponential Smoothing
	20.12 Additional Examples
	Exercises
	Answers
21. Probability Theory
	21.1 Introduction
	21.2 Random Experiment, Outcome, Event
	21.3 Important Terminology
	21.4 Techniques of Counting
	21.5 Classical (or ‘a Priori’) Definition of Probability
	21.6 Theorems of Probability
	21.7 Drawing without Replacement
	21.8 Repeated Trials—Drawing with Replacement
	21.9 Bayes’ Theorem
	21.10 Other Approaches to Probability Theory
	21.11 Set and Probability
	21.12 Axioms of Probability
	21.13 Finite Probability Space and Assignment of Probabilities
	21.14 Finite Equiprobable Sample Space and Classical Definition
	21.15 Conditional Probability
	21.16 Independent Events
	21.17 Additional Examples
	Exercises
	Answers
University of Calcutta Question Paper-2011 (with Hints and Answers)
Log Tables
Index