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Book Review & Overview: Fundamentals of Applied Statistics by S.C. Gupta and V.K. Kapoor

Subject: Statistics & Mathematics
Authors: S.C. Gupta, V.K. Kapoor
Level: Undergraduate & Postgraduate Students
Primary Use: Competitive Exams (IAS, IFS, ISS), University Coursework

. Each chapter typically introduces a mathematical theorem, provides a rigorous proof, and then immediately demonstrates its utility through solved examples. This helps students move from "how" a formula works to "why" it matters. 3. Reliability in Research Book Review & Overview: Fundamentals of Applied Statistics

  1. Introduction to Statistics: Definitions, types of data, scales of measurement, uses and limitations.
  2. Data Collection and Presentation: Sampling, primary vs secondary data, classification, tabulation, frequency distributions, histograms, ogives.
  3. Measures of Central Tendency: Mean (arithmetic, geometric, harmonic), median, mode, partition values (quartiles, percentiles).
  4. Measures of Dispersion: Range, quartile deviation, mean deviation, variance, standard deviation, coefficient of variation.
  5. Moments, Skewness, and Kurtosis: Raw and central moments, Pearson’s and Bowley’s measures, interpretation of skewness and kurtosis.
  6. Correlation and Regression: Scatterplots, correlation coefficients (Pearson’s r, rank correlations), simple and multiple linear regression, regression lines and interpretation, residual analysis.
  7. Probability Theory: Basic probability, axioms, conditional probability, Bayes’ theorem, discrete and continuous distributions.
  8. Probability Distributions: Binomial, Poisson, Normal distributions; properties and applications; approximation between distributions.
  9. Sampling Theory: Concepts of populations and samples, sampling distributions, standard error, Central Limit Theorem.
  10. Estimation Theory: Point and interval estimation, unbiasedness, consistency, efficiency, methods of estimation (method of moments, maximum likelihood).
  11. Hypothesis Testing: Null and alternative hypotheses, Type I/II errors, significance levels, z-test, t-test, chi-square test, F-test, p-values, power of a test.
  12. Analysis of Variance (ANOVA): One-way and two-way ANOVA, partitioning of total variation, assumptions and applications.
  13. Non-parametric Tests: Sign test, Wilcoxon tests, Kruskal–Wallis, Mann–Whitney U test.
  14. Index Numbers and Time Series: Construction methods, uses, smoothing, trend analysis, seasonality, forecasting techniques.
  15. Quality Control & Statistical Applications: Control charts, acceptance sampling (in some editions), applied examples in economics, commerce, and industry.
  16. Multivariate Techniques (introductory): Basic concepts of multivariate distributions, principal component ideas (usually brief).

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Introduction:

Fundamentals of Applied Statistics by S.C. Gupta and V.K. Kapoor is a staple textbook for undergraduate and postgraduate students in India, particularly those preparing for competitive exams like the Indian Statistical Service (ISS) or Civil Services. Introduction to Statistics: Definitions

Statistical Quality Control (SQC): Techniques for monitoring industrial processes and ensuring product standards.

  1. Visit www.sultanchand.com
  2. Search “Fundamentals of Applied Statistics Gupta Kapoor”
  3. Select “e-Book” → purchase → download.
  1. Portability – The physical book is bulky (over 700 pages). A PDF can be carried on a laptop, tablet, or phone.
  2. Cost – New editions cost around ₹600–900 ($8–12 USD) in India, but international shipping makes it expensive abroad.
  3. Out-of-print editions – Some older editions containing specific exercise sets are no longer printed.
  4. Quick searchability – Students preparing for exams need to jump to solved examples on specific topics (e.g., t-test applications).