UPSC Statistics Syllabus For IAS Exam 2024: Know Exam Pattern, Books, and PYQs on our website

UPSC Statistics Syllabus For IAS Exam 2024

UPSC Statistics Syllabus For IAS Exam 2024: 48 In the list of UPSC alternative topics, one of the least preferred subjects is ‘statistical alternative’. This statistics is due to the technical and specific nature of alternative paper. Many candidates hesitate to take data as an alternative subject in UPSC exam due to its equality with mathematics and its complex course.

However, choosing data as an alternative subject provides different benefits to individuals with probability, sampling techniques, data analysis and strong understanding of related concepts. The subject offers the opportunity to score high marks with minimal competition. See alternate about syllabus, advantages, pyq and statistics in this article.

UPSC Statistics Syllabus For IAS Exam 2024
UPSC Statistics Syllabus For IAS Exam 2024

UPSC Statistics Optional Subject For Mains Exam 

The theme of data is related to data. The process involves collecting data, organizing, analyzing and presenting data to achieve meaningful insights. Candidates interested in mathematical subjects and can choose data as optional in search of technical subjects.

Statistics optional subjects usually include in respective graduate courses. Like other alternative letters, the statistics option also includes two papers, paper 1 and paper 2, each of which has 250 marks. Once the candidates have developed a good understanding of fundamental concepts in this option, it is not very challenging to score high marks.

UPSC Statistics Syllabus For IAS Exam Optional

Statistics alternative courses are equally divided into two letters. Paper I focus on subjects such as probability, statistical estimation, co -ordinating analysis and sampling techniques. Exam paper II focuses on statistical computing, industrial data and quantitative economics.

Candidates can download the UPSC Statistics Alternative Course PDF by visiting the official website or by looking at the table below for full subject-wise syllabus. UPSC Statistics

UPSC Statistics Optional Syllabus Paper 1

Paper 1 Statistics Alternative Courses include the theoretical and fundamental concepts of most figures. Statistics alternative Paper 1 has four main subjects distributed among different sub-topics. Here the first paper course of statistics is optional:

Table: UPSC Statistics Optional Syllabus For Paper 2

1. Probability
  • Sample space and events, probability measure and probability space, random variable as a measurable function.
  • Distribution function of a random variable, discrete and continuous-type random variable, probability density function, vector-valued random variable, probability mass function, marginal and conditional distributions, stochastic independence of events and of random variables, conditional expectation, expectation and moments of a random variable, convergence of a sequence of random variable in distribution, in probability, in path mean and almost everywhere, their criteria and inter-relations, Chebyshev’s inequality and Khintchine’s weak law of large numbers, strong law of large numbers, and Kolmogoroffs theorems, probability generating function, characteristic function, moment generating function, inversion theorem, Linderberg and Levy forms of central limit theorem, continuous probability distributions and standard discrete.
2. Statistical Inference
  • Consistency, unbiasedness, efficiency, completeness, ancillary statistics, sufficiency, factorization theorem, exponential family of distribution and its properties, Rao Blackwell and Lehmann-Scheffe theorems, uniformly minimum variance unbiased (UMVU) estimation, Cramer-Rao inequality for single Parameter.
  • Estimation by methods of moments, maximum likelihood, minimum chi-square and modified minimum chi-square, least squares, properties of maximum likelihood and other estimators, prior and posterior distributions, loss function, asymptotic efficiency, risk function, and minimax estimator. Bayes estimators. UPSC Statistics
  • Non-randomised and randomised tests, critical function, MP tests, Neyman-Pearson lemma, monotone likelihood ratio: similar and unbiased tests, UMP tests, UMPU tests for single parameter likelihood ratio test and its asymptotic distribution. Confidence bounds and its relation.
  • Kolmogorov’s test for goodness of fit and its consistency, Wilcoxon signed ranks test and its consistency, sign test, and its optimality, Kolmogorov-Smirnov two-sample test, run test, Wilcoxon-Mann-Whitney test, and median test, along with their consistency and asymptotic normality, are all essential statistical methods for analyzing data and making inferences. UPSC Statistics
  • Wald’s SPRT and its properties, Oc, and ASN functions for tests regarding parameters for Bernoulli, normal, Poisson and exponential distributions. Wald’s fundamental identity.
3. Linear Inference and Multivariate Analysis 
  • Linear statistical models, least squares estimates, Gauss-Markoff theory, theory of least squares and analysis of variance, normal equations, and their precision, test of significance, and interval estimates based on least squares theory in oneway, two-way, curvilinear regression, and three-way classified data, linear regression, regression analysis, and orthogonal polynomials, multiple regression, multiple and partial correlations, multivariate normal distribution, estimation of variance and covariance components, Mahalanobis’s D2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, and principal component analysis.
4. Sampling Theory and Design of Experiments
  • An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, stratified random sampling, simple random sampling with and without replacement, probability sampling designs, cluster sampling, two-stage and multi-stage sampling, systematic sampling and its efficacy, probability proportional to size sampling with and without replacement, two-phase sampling, the Hansen-Hurwitz and the Horvitz Thompson estimators, ratio and regression methods of estimation involving one or more auxiliary variables, non-negative variance estimation with reference to the Horvitz-Thompson estimator, non-sampling errors.
  • Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal observation per cell), RBD, LSD, CRD and their analyses, incomplete block designs, missing plot technique, confounding in factorial experiments, BIBD, concepts of orthogonality and balance, factorial experiments and 24 and 32, split-plot and simple lattice designs, transformation of data Duncan’s multiple range test.

UPSC Statistics Optional Syllabus For Paper 2

Statistics in Paper 2 highlights dynamic subjects such as official data, demographics and psychometry, providing a comprehensive understanding of statistical principles applied in various fields. To score good marks, candidates need to mastered each and each subject of Paper 2 Statistics Alternative Course. The course of paper 2 is as follows:

Table: UPSC Statistics Optional Syllabus For Paper 2

1. Industrial Statistics
  • Process and product control, different types of control charts for variables and attributes, X, R, s, p, np and charts, general theory of control charts, cumulative sum chart. Single, double, multiple, and sequential sampling plans for attributes, OC, ASN, AOQ, and ATI curves, AQL, LTPD, and AOQL, Sampling plans for variables, concepts of producer’s and consumer’s risks, Use of Dodge-Romin tables.
  • Concept of reliability, reliability of series and parallel systems and other simple configurations, failure rate, and reliability functions, renewal density, and renewal function, Failure models: exponential, Weibull, normal, lognormal. Problems in Life Testing of Censored and Truncated Experiments for Exponential Models.
2. Optimization Techniques
  • Different types of models in Operations Research, simulation and Monte-Carlo methods formulation of Linear Programming (LP) problem, their construction, and general methods of solution, simple LP model and its graphical solution, the two-phase method, and the M-technique with artificial variables, the simplex procedure, the duality theory of LP and its economic interpretation, transportation and assignment problems, sensitivity analysis, rectangular games, two-person zerosum games, methods of solution (graphical and algebraic).
  • Replacement of failing or deteriorating items, the concept of scientific inventory management and analytical structure of inventory problems, group and individual replacement policies, simple models with deterministic and stochastic demand with and without lead time, Storage models with special reference to dam types.
  • Homogeneous discrete-time Markov chains, classification of states, and ergodic theorems, homogeneous continuous-time Markov chains, transition probability matrix, Poisson process, elements of queuing theory, M/MI, M/M/K, G/M/l and M/G/1 queues.
  • Solving statistical problems on computer using famous statistical software packages like SPSS.
3. Quantitative Economics and Official Statistics
  • Determination of trend, seasonal, and cyclical components, Box-Jenkins method, ARIMA models, and determination of orders of autoregressive and moving average components, tests for stationary series, forecasting. Commonly used index numbers – Laspeyre’s, Paasche’s, cham-base index number, uses and limitations of index numbers, the index number of wholesale prices, and Fisher’s ideal index numbers, consumer prices, agricultural production, and industrial production, time-reversal, test for index numbers -proportionality, factor-reversal and circular.
  • General linear model, ordinary least square and generalized least squares methods of estimation, consequences, and solutions of multi-collinearity, the problem of multi-collinearity, autocorrelation, and its consequences, heteroscedasticity of disturbances and its testing, the problem of identification-rank and order conditions of identifiability, test for independence of disturbances concept of structure and model for simultaneous equations, two-stage least square method of estimation.
  • Present official statistical system in India relating to population, agriculture, trade and prices, methods of collection of official statistics, their reliability and limitations, industrial production,various official agencies responsible for data collection, principal publications containing such statistics, and their main functions.
4. Demography and Psychometry
  • Demographic data from census, registration, NSS, and other surveys, and uses, definition, and their limitations, construction and uses of vital rates and ratios, measures of fertility, reproduction rates, morbidity rate, complete and abridged life tables, construction of life tables from vital statistics and census returns, standardized death rate, uses of life tables, logistic and other population growth curves, population projection, stable population, quasi-stable population, techniques in estimation of demographic parameters, fitting a logistic curve, standard classification by cause of death, health surveys and use of hospital statistics.
  • Methods of standardisation of scales and tests, Z-scores, standard scores, percentile scores, intelligence quotient and its measurement and uses, T-scores, validity and reliability of test scores and its determination, use of factor analysis and path analysis in psychometry.

UPSC Statistics Optional Subject Pros and Cons

Before choosing any alternative subject, candidates should understand its advantages and disadvantages. This also applies to alternative data. The advantages and disadvantages of choosing data in UPSC CSE Mains exam are given below:

Pros of UPSC Statistics Optional Subject

Statistics provides the following benefits to optional subject candidates:

  • The competition is low and scoring opportunities are good.
  • Low thematic adequacy makes it easy to score high marks after adequate modification and practice.
  • Stable courses that you have prior knowledge is easy to cover.
  • Suitable for those candidates who have studied data during graduation or post graduation.
  • UPSC is the best for candidates targeting the Indian Statistical Service (ISS) exam.

Cons of UPSC Statistics Optional Subject

Candidates can avoid taking this alternative subject in the main examination for the following reasons:

  • Lack of study materials in the market for statistics alternative subjects.
  • Quality data alternative testing chains are not easily available.
  • There is no overlap with other general studies papers, making it difficult for students to balance all subjects of UPSC Main.
  • This requires a lot of self-study and writing practice.

Previous Year’s UPSC Statistics Optional Paper

To understand the nature of questions asked in statistics alternative paper, it is important to take a look at the previous year’s question papers. Alternative UPSC PYQs are good sources of analysis requirements for this subject and practice answer writing for UPSC Main.

Here is a direct link to download year-wise statistics alternative UPSC question paper:

Statistics Optional Previous Year Question Papers
YearPaperDownload Link
2020Statistics Paper IClick Here
Statistics Paper IIClick Here
2021Statistics Paper IClick Here
Statistics Paper IIClick Here
2022Statistics Paper IClick Here
Statistics Paper IIClick Here
2023Statistics Paper IClick Here
Statistics Paper IIClick Here

UPSC Statistics Optional Books

Candidates should ensure that they have quality study material to cover all subjects of alternative statistics course. Keeping in mind the broad course of alternative data, it is highly recommended to refer to standard books. Here is a list of statistics alternative books to prepare for UPSC Mains Exam:

UPSC Statistics Optional Books
Book NameAuthor
An Introduction to Probability Theory & Mathematical StatisticsV K Rohtagi
Introductory Probability and Statistical ApplicationsPaul Meyer
An Outline of Statistical Theory (2 Vol.)A M Goon, M K Gupta, and B. Dass Gupta
Fundamentals of Applied StatisticsS C Gupta and V K Kapoor
Fundamentals of Mathematical StatisticsA C Gupta and V K Kapoor
Fundamentals of Statistics (2 Vol.)A M Goon, M K Gupta, and B Dass Gupta
Sampling TechniquesWilliam G. Cochran
Sampling Theory of Surveys with ApplicationsB. V Sukhatme & B V Sukhatme

How to Prepare for UPSC Statistics Optional Subject?

A good preparation can perform miracles in the coupled quality reference material statistics optional with strategy and dedication. It is possible to score 250+ if the candidates prepare systematically for the UPSC Mains exam with this option. Here are some suggestions for the preparation of alternative statistics in UPSC:

  • Syllabus First: Take a look at the latest Statistics optional paper syllabus and pay attention to subjects for study.
  • PYQ Analysis: Candidates should analyze the previous year’s question papers and note recurring subjects.
  • Fundamental: Start with fundamental concepts and carefully study the subjects of high yield.
  • Mathematics: Relevant infrastructure does not hesitate to modify the subjects.
  • Speed ​​and accuracy: Candidates should practice maximum questions in an examination like environment, as this paper requires a balance of speed and accuracy which can be learned by displaying in the UPSC Main Exam series.
  • Avoid normal answers: Stay specific in your answers as it is a technical theme with certain concepts. Try to use tables, charts and graphs in your reactions.
  • Get help: To improve performance in this optional, seek help wherever possible. Consider joining an alternative UPSC coaching or mentorship program.

UPSC Statistics Optional Subject Success Rate

While some candidates opt for ‘UPSC Statistical Optional’ in UPSC Civil Services Mains Examination, success rate is average. Candidates who have made up their mind to take this alternative, can mention the data available below for statistics, optional UPSC success rate:

Statistics Optional UPSC Success Rate
YearSuccess Rate in UPSCTotal Appeared Candidates Selected Candidates

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