Arithmetic Mean Or Average, Median and Mode

• For discrete data - individual series
• For discrete or ungrouped frequency distribution
• For a continuous or grouped frequency distribution
• Weighted mean/li>
• Combined mean
• Properties of Arithmetic Mean

• For discrete data - individual series
• For an ungrouped frequency distribution
• For a grouped frequency distribution
• Partition values - Quartiles, Deciles and Percentiles

• Individual series
• Discrete series
• Continuous series
• Relationship between Mean, Median and Mode

Measures of dispersion

• Individual series
• Discrete series
• Continuous series

• Individual series - ungrouped data
• Grouped data or Frequency distribution
• Coefficient of mean deviation

• Variance and S.D. for ungrouped data
• Variance and S.D. of a discrete frequency distribution
• Variance and S.D. of a continuous frequency distribution
• Coefficient of Variation
• Algebraic Properties of Standard deviation

Correlation

• Univariate Data
• Multivariate Data
• Bivariate Data

• Bivariate Frequency Distribution
• Two way Frequency Tables

• Perfect Correlation
• Positive or Direct Correlation
• Negative or Indirect Correlation
• Linear and nonlinear correlation

• Perfect positive correlation
• Perfect negative correlation
• Degree of correlation
• No correlation

• Covariance
• Correlation Coefficient
• Karl Pearsons Correlation Coefficient
• New formula
• Modified Formula

• Spearman's method
• Kendall's method

Regression

• Dependent Variables
• Independent Variables

• Definition & Obtaining the Regression Line of Y On X
• Definition & Obtaining the Regression Line of X On Y
• Theorem : Coefficient of Regression of Y On X
• Properties of Regression Coefficient

• Error Of Prediction - Theorem
• Error Of Prediction - Examples

Random Experiment and Sample Spaces

• Types of Events
• Exhaustive Events and Mutually Exclusive Events
• Euler's Venn diagrams
• Probability of an Event
• Classical and Static definition of Probability
• Probability of equally likely events
• Conditional Probability
• Independent and dependent events

• Addition theorem on Probability
• Multiplication theorem on Probability
• Baye's theorem

• Random variable - Discrete and continuous
• Probability distributions of random variable
• Distribution functions
• Mean, variance and standard deviation of random variable
• Probability density function

Distribution Functions & Mathematical Expectation

• Distribution Functions - Definition
• Distribution Functions - Problems

• Expectation of a Discrete Random Variable
• Interpretation of E(X)
• Particular cases
• Addition Theorem
• Multiplication Theorem
• Some More Theorems

Moments, Skewness & Kurtosis

• Moments of a variable about a Point ( or an Arbitrary Value )
• Moments of a variable about the Mean ( Or Central Moments )
• Express Central Moments in terms of Moments about a Point
• Express Moments about a Point 'A' in terms of Central Moments
• Sheppard's Correction - Moments of Grouped Frequency Distribution
• Effect of Change of origin on Moments
• Moments - Problems

• Definition
• Skewed Distribution
• Positive Skewness
• Negative Skewness
• Measures of Skewness
• Relative Measures of Skewness
• Skewness - Problems

• Definitions of Hump & Kurtosis
• Kurtosis - Problems

Theoretical probability Distributions

• Definition & Probability Density Function
• Conditions for applying the Binomial Theorem
• Mean, Variance and Standard deviation of Bonomial distribution
• Recurrence Relation for Binomial Distribution

• Examples of Events following Poisson Distribution
• Poisson approximation of Binomial Distribution
• Mean and Variance of Poisson Distribution
• Recurrence relation for Poisson Distribution

• PDF of Normal Distribution, Normal Curve & Properties of Normal
• Standard Normal Distribution Or Z-Distribution
• Finding the Probability when limits of Standard Normal Variate
• Normal Distribution - Problems