CSS Syllabus — Statistics

Total Marks: 100

Part – I — 50 Marks

I. Descriptive Statistics

• Definition, importance and scope of Statistics

• Descriptive and Inferential Statistics

• Presentation of Data

• Tables, Graphs and Charts

• Stem-and-Leaf Diagram

• Box-and-Whisker Plots

• Measures of Central Tendency / Location

• Measures of Dispersion / Variability

• Measures of Skewness

• Measures of Kurtosis

II. Basic Probability

• Basic Probability Concepts

• Additive and Multiplicative Laws of Probability

• Joint and Marginal Probabilities

• Conditional Probability and Statistical Independence

• Bayes’ Rule

• Concept of a Random Variable

• Mathematical Expectations

• Discrete and Continuous Random Variables

• Probability Distributions

• Mean and Variance of a Discrete Random Variable

III. Probability Distributions

• Discrete and Continuous Probability Distributions

• Properties and Applications of:

  • Binomial Distribution

  • Poisson Distribution

  • Hypergeometric Distribution

  • Normal Distribution and its properties

• Standard Normal Curve

• Normal Approximation to:

  • Binomial Distribution

  • Poisson Distribution

IV. Regression Analysis & Correlation Analysis

• Concepts of Regression and Correlation and their applications

• Simple and Multiple Linear Regression (up to three variables)

• Estimation of Parameters

• Method of Least Squares

• Inference regarding Regression Parameters

• Correlation

• Correlation Coefficient

• Properties of Correlation Coefficient

• Inference regarding Correlation Coefficient

• Partial Correlation

• Multiple Correlation (up to three variables)

V. Non-Parametric Methods

• Parametric versus Non-Parametric Tests

• When to use Non-Parametric Procedures

One-Sample Tests

• Sign Test

• Wilcoxon Signed-Rank Test

• Kolmogorov–Smirnov Test

• Run Test

Tests for Two Related Samples

• Sign Test

• Run Test

• Chi-Square Test

Tests for Two Independent Samples

• Mann–Whitney Test

• Kolmogorov–Smirnov Test

Part – II — 50 Marks

I. Sampling & Sampling Distributions

• Population and Sample

• Advantages of Sampling

• Sampling Design

• Probability and Non-Probability Sampling Techniques

Probability Sampling

• Simple Random Sampling

• Stratified Sampling

• Systematic Sampling

• Cluster Sampling

• Multiple Sampling

• Multistage Sampling

Non-Probability Sampling

• Purposive Sampling

• Quota Sampling

• Convenience Sampling

• Accidental Sampling

Sampling Distributions

• Sampling with and without Replacement

• Application of Central Limit Theorem in Sampling

• Sampling Distribution of:

  • Mean

  • Difference between Two Means

  • Proportion

  • Difference between Two Proportions

  • Variance

II. Statistical Inferences

Estimation

• Point Estimation

• Properties of a Good Estimator

• Interval Estimation

• Interval Estimation of Population Mean

• Large and Small Sample Confidence Intervals for Population Mean

Hypothesis Testing

• Types of Errors

• Hypothesis Testing for Population Mean

• Inferences for Two Population Means

• Inferences for the Mean of Two Normal Populations Using Independent Samples (variances assumed equal)

• Inference for Two Population Means Using Paired Samples

• Inferences for Population Proportions

• Confidence Intervals and Hypothesis Testing for Population Proportion

• Inferences for Two Population Proportions Using Independent Samples

• Estimation of Sample Size

Analysis of Categorized Data

• Goodness-of-Fit Tests

• Contingency Tables

• Test of Independence in Contingency Tables

III. Design of Experiments

• One-Way Analysis of Variance (ANOVA)

• Two-Way Analysis of Variance (ANOVA)

• Design of Experiments

• Concepts of:

  • Treatment

  • Replication

  • Blocking

  • Experimental Units

  • Experimental Error

• Basic Principles of Design of Experiments

Experimental Designs

• Description, Layout and Statistical Analysis of Completely Randomized Design (CRD)

• Description, Layout and Statistical Analysis of Randomized Complete Block Design (RCBD)

• Multiple Comparison Tests

  • LSD Test

IV. Population Analysis & Vital Statistics

Population and Demographic Methods

• Population and Demographic Methods

• Sources of Demographic Data

• Basic Demographic Measures

• Sex Ratio

• Child-Women Ratio

• Vital Index

• Crude and Specific Birth Rates

• Crude and Specific Death Rates

• Total Fertility Rate

• Net Reproduction Rate

Official Statistics

• Statistical Systems in Pakistan

• Functions of Statistics Division and Bureaus of Statistics

• National Income

• Gross Domestic Product (GDP)

• Saving and Wealth

• Index Numbers

Suggested Readings