Statistics Mock Tests

Statistics Syllabus for WB SLST 2025 (Class XI-XII)

This syllabus provides a comprehensive overview of key statistical concepts and techniques essential for understanding and applying statistics at the senior secondary level. It is designed to build a strong foundation in probability, data analysis, inference, and applied statistics with an emphasis on examination readiness and practical applications.

1. Probability Theory

• Fundamentals of Probability: Classical and axiomatic definitions, sample spaces, events, and probability rules.
• Bayes' Theorem: Conditional probability and applications in real-world problems.
• Random Variables: Discrete and continuous types, probability mass and density functions.
• Probability Distributions: Common distributions, generating functions (moment generating functions, probability generating functions).
• Limit Theorems: Law of Large Numbers and Central Limit Theorem with practical examples.

2. Descriptive Statistics & Distributions

• Measures of Central Tendency: Mean, median, mode, and their properties.
• Measures of Dispersion: Range, variance, standard deviation, mean deviation, and coefficient of variation.
• Skewness and Kurtosis: Concepts and calculation methods to describe data shape.
• Common Distributions: Binomial, Poisson, and Normal distributions with parameters and applications.
• Regression and Correlation: Simple linear regression, multiple regression, correlation coefficients, and interpretation.
• Multivariate Analysis: Introduction to analyzing multiple variables simultaneously.

3. Sampling Distributions

• Sampling Concepts: Population vs. sample, sampling methods, and sampling errors.
• Key Sampling Distributions: Chi-square (χ), Student's t, and F distributions with properties and applications.
• Order Statistics: Definitions and importance in statistics.
• Advanced Tools: Hotellings T statistic, principal component analysis, and Mahalanobis distance for multivariate data analysis.

4. Estimation & Hypothesis Testing

• Point and Interval Estimation: Methods of estimation, confidence intervals, and interpretation.
• Cramér-Rao Inequality: Lower bound for variance of estimators.
• Neyman-Pearson Lemma: Framework for most powerful tests.
• Likelihood Ratio Tests: Formulation and applications.
• Sequential Testing: Walds Sequential Probability Ratio Test (SPRT) and its practical use.

5. Special Tests & Transformations

• Exact, Large-Sample, and Nonparametric Tests: Overview and when to apply each.
• Analysis of Variance (ANOVA): One-way and two-way ANOVA for comparing means.
• Variance Stabilizing Transformations: Techniques to stabilize variance in data analysis.
• Chi-square Based Tests: Goodness-of-fit, test for homogeneity, and test for independence with examples.

6. Applied Statistics

• Index Numbers: Construction and uses in economics and social sciences.
• Time Series Analysis: Components, trend analysis, and forecasting methods.
• Demand Analysis: Basic concepts and statistical tools.
• Demography: Birth and death rates, life tables, and population studies.
• Experimental Designs: Completely Randomized Design (CRD), Randomized Block Design (RBD), factorial experiments, and their applications.
• Sampling Methods: Various sampling techniques and their practical considerations.
• Quality Control: Control charts, acceptance sampling, and statistical process control techniques.

Important Notes: Focus on understanding concepts with practical examples. Practice solving problems related to distributions, hypothesis testing, and applied statistics to excel in examinations. Emphasize interpretation of results and real-world applications.