UPSC Statistics Syllabus for IAS Optional Paper 2023

The Union Public Service Commission has released the official notification for the detailed UPSC Statistics Syllabus 2023 Syllabus. The UPSC offers 48 optional subjects and Statistics is one of them. Statistics is part of mathematics and hence, requires immense amounts of practice and revision.

The UPSC exam is a three-stage process. Candidates have to attempt a prelims exam, a mains and an interview.
Statistics for UPSC civil services exam focuses more on data collection, analysis, collection, organization, interpretation.
There’s no subjectivity in this subject and it’s considered as a part of mathematics.
The candidates who have a good grasp on mathematical theories and application can pick statistics as their optional subject.
Study material for statistics is widely available but one must pick their reference books wisely.

UPSC statistics syllabus

It is crucial for the aspirants to assess their aptitude in the particular subject and then pick it as an optional subject. Here, in this article, we present in detail the UPSC statistics syllabus optional, exam pattern, best reference books and exam preparation tips.

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UPSC Statistics Syllabus for IAS Mains Exam – Paper I & II

Initial preparation of the exam starts with a thorough knowledge of the syllabus and the exam pattern. Mentioned below is the UPSC statistics syllabus for optional paper 1 and paper 2 of IAS mains:

Optional Paper I of Statistics Subject – 250 Marks

Download the Latest UPSC Statistics Syllabus PDF in Hindi Here!

Topic	Sub-Topic
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 mass function, probability density function Vector-valued random variable, marginal and conditional distributions, stochastic independence of events and of random variables, expectation and moments of a random variable, conditional expectation, convergence of a sequence of random variable in distribution, in probability, in p-th mean and almost everywhere, their criteria and inter-relations Borel-Cantelli lemma, Chebyshev’s and Khinchine‘s weak laws of large numbers, strong law of large numbers and kolmogorov’s theorems, Glivenko-Cantelli theorem, probability generating function, characteristic function, inversion theorem Laplace transform, related uniqueness and continuity theorems, determination of distribution by its moments. Lindenberg and Levy forms of central limit theorem, standard discrete and continuous probability distributions, their inter-relations and limiting cases, simple properties of finite Markov chains
Statistical Inference	Consistency, unbiasedness, efficiency, sufficiency, minimal sufficiency, completeness, ancillary statistic, factorization theorem, exponential family of distribution and its properties, uniformly minimum variance unbiased (UMVU) estimation Rao-Blackwell and Lehmann-Scheffe theorems, Cramer-Rao inequality for single and several-parameter family of distributions, minimum variance bound estimator and its properties, modifications and extensions of Cramer-Rao inequality Chapman- Robbins inequality, Bhattacharyya’s bounds, estimation by methods of moments, maximum likelihood, least squares, minimum chi-square and modified minimum chi-square, properties of maximum likelihood and other estimators, idea of asymptotic efficiency, idea of prior and posterior distributions Bayes estimators, Non-randomised and randomised tests, critical function, MP tests, Neyman-Pearson lemma, UMP tests, monotone likelihood ratio, generalised Neyman-Pearson lemma, similar and unbiased tests UMPU tests for single and several-parameter families of distributions, likelihood rotates and its large sample properties, chi-square goodness of fit test and its asymptotic distribution Confidence bounds and its relation with tests, uniformly most accurate (UMA) and UMA unbiased confidence bounds. Kolmogorov’s test for goodness of fit and its consistency, sign test and its optimality Wilcoxon signed- ranks test and its consistency, Kolmogorov-Smirnov two-sample test, run test, Wilcoxon-Mann- Whiltney test and median test, their consistency and asymptotic normality Wald’s SPRT and its properties, OC and ASN functions, Wald’s fundamental identity, sequential estimation. Wald’s SPRT and its properties, OC and ASN functions for tests regarding parameters for Bernoulli, Poisson, normal and exponential distributions. Wald’s fundamental identity
Linear Inference and Multivariate Analysis	Linear statistical models, theory of least squares and analysis of variance, Gauss-Markoff theorem, normal equations, least squares estimates and their precision, test of significance and interval estimates based on least squares theory in one-way, two-way and three-way classified data Regression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, regression diagnostics and sensitivity analysis, calibration problems, estimation of variance and covariance components MINQUE theory, multivariate normal distribution, Mahalanobis;’ D2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, one-way MANOVA, principal component analysis, elements of factor analysis
Sampling Theory and Design of Experiments	An outline of fixed-population and super-population approaches, distinctive features of finite population sampling, probability sampling designs, simple random sampling with and without replacement Stratified random sampling, systematic sampling and its efficacy for structural populations, cluster sampling, two-stage and multi-stage sampling, ratio and regression, methods of estimation involving one or more auxiliary variables, two-phase sampling, probability proportional to size sampling with and without replacement The Hansen-Hurwitz and the Horvitz-Thompson estimators, non-negative variance estimation with reference to the Horvitz-Thompson estimator, non- sampling errors, Warner’s randomised response technique for sensitive characteristics Fixed effects model (two-way classification) random and mixed effects models (two-way classification per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial designs : 2n, 32 and 33, confounding in factorial experiments, split-plot and simple lattice designs

Download the Latest UPSC Statistics Syllabus PDF Here!

Optional Paper-II of Statistics Subject – 250 Marks

Topic	Sub-Topic
Industrial Statistics	Process and product control, general theory of control charts, different types of control charts for variables and attributes, X, R, s, p, np and c charts, cumulative sum chart, V-mask, single, double, multiple and sequential sampling plans for attributes OC, ASN, AOQ and ATI curves, concepts of producers and consumer’s risks, AQL, LTPD and AOQL, sampling plans for variables, use of Dodge- Romig and Military Standard tables. Concepts of reliability, maintainability and availability, reliability of series and parallel systems and other simple configurations Renewal density and renewal function, survival models (exponential), Weibull, lognormal, Rayleigh, and bath-tub), different types of redundancy and use of redundancy in reliability improvement, problems in life-testing, censored and truncated experiments for exponential models
Optimization Techniques	Different, types of models in Operational Research, their construction and general methods of solution, simulation and Monte-Carlo methods, the structure and formulation of linear programming (LP) problem, simple LP model and its graphical solution The simplex procedure, the two-phase method and the M-technique with artificial variables, the duality theory of LP and its economic interpretation, sensitivity analysis, transportation and assignment problems Rectangular games, two-person zero-sum games, methods of solution (graphical and algebraic). Replacement of failing or deteriorating items, group and individual replacement policies, concept of scientific inventory management and analytical structure of inventory problems Simple models with deterministic and stochastic demand with and without lead time, storage models with particular reference to dam type Homogeneous discrete-time Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuous-time Markov chains Poisson process, elements of queueing theory, M/M/1, M/M/K, G/M/1 and M/G/1 queues. Solution of statistical problems on computers using well known statistical software packages like SPSS
Quantitative Economics and Official Statistics	Determination of trend, seasonal and cyclical components, Box-Jenkins method, tests for stationery of series, ARIMA models and determination of orders of autoregressive and moving average components, forecasting Commonly used index numbers-Laspeyres, Paashe’s and Fisher’s ideal index numbers, chain-base index number uses and limitations of index numbers, index number of wholesale prices, consumer price index number, index numbers of agricultural and industrial production, tests, for index Numbers, proportionality test, time-reversal test, factor-reversal test, circular test and dimensional invariance test, General linear model, ordinary least squares and generalised least squares methods of estimation, problem of multicollinearity, consequences and solutions of multicollinearity Autocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for Independence of disturbances, Zellner’s seemingly unrelated regression equation model and its estimation Concept of structure and model for simultaneous equations, problem of identification-rank and order conditions of identifiability, two-stage least squares method of estimation Present official statistical system in India relating to population, agriculture, industrial production, trade and prices, methods of collection of official statistics, their reliability and limitation and the principal publications containing such statistics, various official agencies responsible for data collection and their main functions
Demography and Psychometry	Demographic data from census, registration, NSS and other surveys, and their limitation and uses, definition, construction and uses of vital rates and ratios, measures of fertility, reproduction rates, morbidity rate, standardized death rate, complete and abridged life tables, construction of life tables from vital statistics and census returns, uses of life tables Logistic and other population growth curves, fitting a logistic curve, population projection, stable population theory, uses of stable population and quasi-stable population techniques in estimation of demographic parameters, morbidity and its measurement, standard classification by cause of death Health surveys and use of hospital statistics. Methods of standardisation of scales and tests, Z-scores, standard scores, T-scores, percentile scores, intelligence quotient and its measurement and uses, validity of test scores and its determination, use of factor analysis and path analysis in psychometry

Check the detailed UPSC IAS Mains Syllabus here.

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UPSC Statistics Exam Pattern 2023

The UPSC exam has three stages of examination viz. prelims, mains and interview. The UPSC IAS mains exam consists of 9 papers, out of which 2 are for optional subjects. The candidates are given a choice of 48 optional subjects to choose from. Here are the details about the UPSC statistics exam pattern for IAS mains:

There will be 2 papers for the statistics optional subject in UPSC IAS Mains.
Each paper would comprise 250 marks, which makes it 500 marks in total.
The time duration to attempt the UPSC statistics paper is 3 hours.
Each paper would have objective answer-type questions.
There is no negative marking.

Sr. No.	IAS Mains Papers	Subject	Marks
1.	Paper VI	Optional Subject Paper-I	250
2.	Paper VII	Optional Subject Paper-II	250
TOTAL			500
Time Duration			3 hours

Check the detailed UPSC IAS exam pattern here.

How to Prepare for UPSC Statistics Optional Subject Paper ?

Statistics is a subject of its own nature, candidates who are certain about the subject should only pick it as an optional one. The candidates should do exceptionally well in their optional subject. Statistics demands persistence practice, conceptual clarity and logical approach. Some of the best ways to prepare for the UPSC statistics syllabus are given below:

As UPSC Statistics is a part of Mathematics, the candidates are required to practice and revise this subject a lot.
Jot down a strategic topic wise timetable and follow it obediently.
It’s mandatory to solve previous years’ question papers and to appear for various mock tests and to attempt the UPSC civil services test series.
Reference books play a vital role. So, the aspirants must cling to a few but the best books, this helps in better understanding and efficient learning.
Candidates must keep a track of their errors in the test series, analyse their weak points and then must work on it accordingly.

Prepare for the exam using the UPSC IAS mains strategy here.

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UPSC Statistics Previous Years’ Question Papers

So that candidates are fully prepared for the UPSC Statistics Syllabus, here are some previous years papers which will help the candidates get an actual interpretation of the examination and know about the type of questions which they can expect under the IAS Mains Statistics section. The candidates must test their aptitude and be aware of their strengths as well as weak assets. Solving UPSC Statistics previous year’s question papers help in time management and recognition of errors that can be corrected.

IAS Statistics Paper 1	Statistics Paper-I PDF Download
IAS Statistics Paper 2	Statistics Paper-II PDF Download

Check some more UPSC IAS Previous Year’s Question Papers for other subjects here!

Books to Refer for UPSC Statistics Syllabus

Some of the best books to study the complete UPSC Statistics optional subject are mentioned below:

An Introduction to Probability Theory and Mathematical Statistics by V K Rohtagi
Basics of Applied Statistics – S C Gupta and V K Kapoor
Basics of Statistics (2 Vol.) – A M Goon, M K Gupta, and B Dass Gupta
Early on Probability and Statistical Applications – Paul Meyer
Basics of Mathematical Statistics – A C Gupta and V K Kapoor

Check Related UPSC Syllabus for Other Subjects
UPSC Geography Optional Syllabus	UPSC History Optional Syllabus
UPSC Economics Optional Syllabus	UPSC Agriculture Optional Syllabus
UPSC Electrical Engineering Optional Syllabus	UPSC Law Syllabus
UPSC Geology Syllabus	UPSC Political Science Syllabus
UPSC Public Administration Syllabus	UPSC Sociology Optional Syllabus

This was a detailed article about the UPSC Statistics Syllabus. To start the preparation for your examination, download the Testbook App and get access to world-class educations, mock tests, etc.

UPSC Statistics Syllabus 2023 FAQs

Can Candidates from any background choose statistics as their optional subject for the UPSC IAS Exam?

The candidates having majors in mathematics can choose statistics as their optional subject.

Is UPSC Statistics subject a part of Mathematics?

Yes, UPSC Statistics is a major part of mathematics and focuses on mathematical application.

What are the total marks for the UPSC IAS Statistics paper?

The UPSC statistics optional paper for the civil services exam is divided into Paper 1 & 2. Each paper carries 250 marks each for a total of 500 marks.

What is the duration of the UPSC Statistics optional Exam?

Every UPSC optional subject for IAS exam is allotted 3 hours of duration.

Are there any changes in the UPSC IAS Statistics syllabus as compared to last year?

No, there has been no major change in the statistics syllabus as compared to the previous years.

When should one start preparing for the UPSC Statistics Exam?

Statistics Syllabus for IAS optional requires a high level of proficiency, and an effective Optional Strategy. Aspirants should solve questions from previous years’ UPSC question papers as well as participate in mock tests Testbook for preparation.

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