Chapter 6 Simple Correlation and

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1 Contents Chapter 1 Introduction to Statistics Meaning of Statistics... 1 Definition of Statistics... 2 Importance and Scope of Statistics... 2 Application of Statistics... 3 Characteristics of Statistics... 4 Functions of Statistics... 5 Limitations of Statistics... 5 Exercise 1 (A)... 6 Data Collection... 6 Introduction... 6 Types of Data... 6 Sources of Primary Data... 7 Sources of Secondary Data... 8 Methods of Collection of Primary Data... 8 Precautions in the use of Secondary Data Problems Involved in Collecting the Primary Data Problems in Collecting Secondary Data Differences between Primary Data and Secondary Data Exercise 1 (B) Chapter 2 Classification and Presentation of Data Raw Data Classification Needs of Classification Types of Classification Variables Frequency Use of Symbols Frequency Distribution Univariate Frequency Distribution Chapter 3 Open Ended Classes and Close Ended Classes Methods of Converting Inclusive Classes into Exclusive Classes Method of Converting Mid Values into Class Intervals Cumulative Frequency Distribution Bivariate Frequency Distribution Tabulation of Data Difference between Classification and Tabulation Parts of Tabulation Structure of a Table Simple and Complex Table Exercise 2 (A) Introduction Difference between Diagrams and Graphs Essentials of a Good Diagram Types of Diagrams Bar Diagrams Angular Diagram or Circular Diagram or Pie Chart Graphical Presentation Exercise 2 (B) Measures of Central Tendency Introduction Definition Characteristics of a Good Measure of Central Tendency or an Average Types of Measure of Central Tendency Arithmetic Mean Geometric Mean Harmonic Mean (HM) Weighted Harmonic Mean Median (Md) Partition Values Mode (M 0) Empirical Relation between Mean, Median and Mode Characteristics of a Good Statistical Average List of Important Formulae Exercise

2 Chapter 4 Measures of Dispersion Introduction Definitions Objectives of Measuring the Dispersion Method of Measuring the Measures of Dispersion Absolute and Relative Measures Characteristics of a Good Measure of Dispersion Range Quartile Deviation or Semi-inter Quartile Range Mean Deviation Coefficient of M.D Standard Deviation Coefficient of Standard Deviation Coefficient of Variation Lorenz Curve List of Important Formulae Exercises Chapter 5 Skewness, Kurtosis and Moments Introduction Skewness Absolute Measures of Skewness Methods of Studying Coefficient of Skewness (Sk) Kurtosis Definition Measure of Kurtosis Moments Central Moments Raw Moments Relation between Central Moments and Raw Moments 197 Skewness based on Moments Kurtosis based on Moments Mean, Variance, Skewness and Kurtosis in Terms of Moments Five Number Summary Box and Whisker Plot (Boxplot) List of Important Formulae Exercises Chapter 6 Simple Correlation and Regression Analysis Introduction Correlation Definition Importance Correlation and Causation Types of Correlation Positive and Negative Correlation Linear and Non-Linear Correlation Simple, Partial and Multiple Correlation Methods of Studying Simple Correlation Scatter Diagram Karl Pearson's Coefficient of Correlation Bivariate Correlation Method Properties of Correlation Coefficient Interpretation of Correlation Coefficient Probable Error (P.E.) Karl Pearson's Correlation in Bivariate Frequency Table Merits and Demerits of Karl Pearson's Coefficient of Correlation Rank Correlation Properties of Rank Correlation Coefficient Methods of Studying Rank Correlation Coefficient Regression Analysis Uses of Regression Analysis Comparison of Correlation and Regression Analysis Regression Equation (Lines of Regression) Alternative Method to Calculate Regression Equations 259 Calculation of Regression Coefficients Properties of Regression Coefficients Sum of Squares Decomposition Coefficient of Determination List of Important Formulae Exercises

3 Chapter 7 Analysis of Time Series Introduction Purpose of Time Series Anaysis Components of Time Series Time Series Decomposition Models Multiplicative Model Additive Model Methods of Measurement of Trend in Time Series Graphical or Freehand Curve Method Semi-Average Method Moving Average Method Method of Least Squares Shifting of the Origin Conversion of annual Trend Equation to Monthly or Quarterly Trend Equation Seasonal Variation and Seasonal Indices Measurement of Seasonal Variations Method of Simple Averages Ratio to Moving Average Method Multiplicative Model Additive Model Exercises Chapter 8 Index Numbers Introduction Types of Index Number Problems in the Construction of Price Index Number Characteristics of Index Numbers Uses of Index Numbers Notations and Terminology Methods of Constructing Index Number Price Index Number Unweighted Price Index Number Weighted Price Index Number Quantity Index Number Unweighted Quantity Index Number Weighted Quantity Index Number Value Index Number Test of Consistency of Index Number Consumer s Price Index Number Construction of cost of Living index Numbers Base Shifting Deflating of the Index Number List of Important Formulae Exercises Chapter 9 Probability Introduction Basic Terms used in Probability Theory Types of Events Permutation and Combination Permutation Combination Definition of Probability Mathematical or Classical or Priori Approach Statistical or Empirical or Relative Frequency Approach 361 Subjective Approach Axiomatic Approach Exercise 9(A) Theorems of Probability Additive Law of Probability Multiplicative Law of Probability Multiplicative Theorem of Probability Baye's Theorem Definition Exercise 9(B) Chapter 10 Sampling and Estimation Introduction Sampling Sampling Frame Census versus Sample Enumeration Principles of Sampling Objectives of Sampling Types of Sampling Types of Random Sampling (Probability Sampling)

4 Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Multistage Sampling Types of Non-random Sampling (Non-probability Sampling) Judgment Sampling Convenience Sampling Quota Sampling Census vs. Sampling Sampling Distribution of a Statistic Standard Error (S.E.) of a Statistic Utility of Standard Error (S.E.) Sampling and Non- Sampling Error Sampling Errors Non Sampling Errors Estimation Introduction Types of Estimates Exercise Chapter 11 Quantitative Analysis Introduction to Quantitative Analysis Application of Management Science Introduction to Decision Making Important Terminologies Decision-making Environment Decision Making Under Risk Expected Profit with Perfect Information (EPPI) Marginal Analysis Approach Exercise 11(A) Linear Programming Linear Inequalities in Two Variables Solution Set of an Inequality Procedure of Graphing a Linear Inequality System of Linear Inequalities Exercise 11(B) Chapter 12 Determinants Determinants Value of Determinant of Order Value of Determinant of Order Value of Determinant of Order Exercise 12(A) Properties of Determinants Systems of Linear Equations Cramer's Rule (Two Unknowns) Cramer's Rule (Three Unknowns) Equilibrium Condition Exercise 12(B) Chapter 13 Matrices Introduction Matrices Notations Sizes of Matrices Types of Matrices Algebra of Matrices Equal Matrices Addition of Matrices Scalar Multiplication of a Matrix Subtraction of Matrices Multiplication of Matrices Properties of Matrix Addition and Multiplication Transpose of a Matrix Properties of Transpose of a Matrix Exercise 13(A) Determinant of a Square Matrix Cofactors and Matrix of Cofactors Adjoint Matrix Singular or Non-Singular Matrix Inverse of Matrix Methods of Determining Inverse Matrices

5 Adjoint Matrix Method Definition Method System of Liner Equation Inverse Matrix Method Exercise 13(B) TU Model Questions References