Syllabus

About Syllabus

Exploring Data

  • Basics

    • Variables,
    • Population vs sample,
    • Central tendency,
    • Variability,
    • Position
  • Charts and Graphs

    • Patterns in data
    • Dot plots
    • Histograms
    • Stem plots
    • Box plots
    • Cumulative plots
    • Scatter plots
    • Comparing data sets
  • Regression

    • Measurement scales
    • linear correlation
    • linear regression
    • Residual analysis
    • Transformations,
    • Influential points
    • Testing of regression slope and intercept
    • Regression Analysis
    • Testing of significance of regression equation
    • Multiple regression analysis
    • Confidence interval for conditional mean of the response variable
    • Prediction interval for an observed value of the response variable
  • Categorical data

  • One-way tables, Two-way tables

Descriptive Statistics

  • Data Condensation

    • Classification of DataClassification of Data
    • Classes
    • Frequency
    • Individual data
    • Discrete Data
    • Continuous / Grouped Data
  • Measure of Central tendency

    • Arithmetic Mean
    • Median
    • Mode
    • Harmonic mean
    • Geometric Mean
    • Weighted Mean
    • Trimmed Mean
    • Quartiles
    • Deciles
    • Percentiles
  • Measure of Dispersion

    • Range
    • Coefficient of Range
    • Quartile deviation
    • Coefficient of quartile deviation
    • Variance
    • Standard deviation
    • Coefficient of Variation (CV).
  • Skewness and Kurtosis

    • Types of Skewness and its measures
    • Types of Kurtosis and its measures
  • Moments

    • Raw Moments
    • Central Moments
    • Relation between raw and central moments.

Probability and Probability Distributions

  • Surveys

    • Data collection
    • Sampling methods
    • Bias in surveys
  • Experiments

    • Introduction to experiments
    • Set
    • Subset
    • Sample space
    • Events and its types,
    • Set Identities.
  • Probability

    • Methods of Counting
    • Permutation
    • Combination
    • Probability introduction
    • Rules of probability
    • Theorems on probability.
  • Random variables

    • Introduction
    • Distributions
    • Mean and variance
    • Independence.
  • Discrete variables and distributions 

    • Bernoulli Distribution
    • Binomial Distribution
    • Negative Binomial Distribution
    • Discrete Uniform Distribution
    • Poisson Distribution
    • Geometric Distribution
    • Hypergeometric Distribution
    • Multinomial Distribution
  • Continuous variables

    • Continuous Uniform Distribution
    • Exponential Distribution
    • Normal Distribution
    • Standard normal Distribution
    • t Distribution,
    • Chi-square Distribution
    • F  Distribution
    • Beta Distribution
    • Gamma Distribution
    • Cauchy  Distribution
    • Lognormal Distribution
    • Weibull Distribution
    • Pareto Distribution
  • Sampling distributions

    • Sampling distribution
    • Sampling distribution of Mean
    • Sampling distribution of Proportion
    • Sampling distribution of Variance/Standard Deviation
    • Difference between proportions
    • Difference between means
    • Differnce between Variances

Statistical Inference

  •  Estimation:

    • Estimation problems
    • Standard error
    • Margin of error
    • Confidence intervals for:
      • Proportions
      • Difference between proportions
      • Mean
      • Difference between means
      • Difference between pairs
      • Regression slope
      • Correlation
      • Variance
      • Standard Deviation
  •  Hypothesis testing:

    • Hypothesis test introduction,
    • How to test (Procedure)
    • Type I-Error
    • Type II-Error
    • Power of test
  • Hypothesis tests Procedures:

    • Proportions
    • Difference between proportions
    • Mean Difference between means
    • Difference between pairs (Paired t test)
    • Goodness of fit test, Homogeneity
    • Chi square test of independence
    • Chi-square test of Variance and Standard Deviation
    • F test for Equality of Variances
    • ANOVA

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