Explore Our Affordable Courses

Click Here

UPSC Statistics Optional: Exam Pattern, Syllabus, Books, and PYQs

Visakha Prashar August 21, 2023 02:00 14014 0

Find out everything you need to know about UPSC Statistics Optional, including the exam pattern, syllabus, previous year question papers, recommended books.

UPSC Statistics Optional: Exam Pattern, Syllabus, Books, and PYQs

UPSC exam is one of the prestigious exams in India and UPSC preparation involves optional subjects in its mains examination choosing the right optional subject is a critical decision that has a direct impact on one’s chances of success in the exam. Among the various options available in the given list of UPSC optional subject list. In this article we will try to explore various dimensions of statistics optional and analyse its syllabus, question papers, and resources that can help in preparation.

Statistics Optional for UPSC Mains

Out of 48 subjects mentioned in the list of UPSC Mains, Optional subject Statistics is one of the preferred subjects who have an educational background of statistics. The Statistics optional subject for the UPSC examination covers key concepts such as descriptive statistics, probability theory, statistical inference, regression analysis, time series analysis, and sampling techniques. 

Candidates are expected to understand how to summarize data, analyze probability distributions, draw conclusions from sample data, explore relationships between variables, interpret time-based data, and employ appropriate sampling methods.  These concepts are essential for candidates aiming to excel in this optional subject and effectively apply statistical principles in various domains.

Exam Pattern Of Statistics Optional Paper for UPSC Mains

The Statistics Optional Paper generally consists of two papers – Paper I and Paper II. Both papers are designed to assess the candidate’s understanding of concepts and their analytical abilities. Each paper is allocated 250 marks. Paper I is asked in two sections. Both sections have four questions. Question 1 from section 1 and Question 5 from section 2 are compulsory. Out of the remaining 6 questions, candidates are allowed to choose their questions. Here, Candidates have to apply their strategy by picking the most mark-fetching questions where they feel they can write the best answer. Here is the exam pattern for Statistics optional UPSC: 

UPSC Statistical Optional Exam Pattern
Particular Details
Total Papers Two, Paper I and Paper II
Total Marks 500 (250 Each)
Time allowed 3 Hours for each paper
Sections Section A and Section B
Questions Total 8 questions with subparts
Compulsory Question Question No. 1 and 5
Marks Distribution 10, 15, and 20 marker questions

Statistics Optional Syllabus for UPSC Papers 1 and 2

The Statistics optional syllabus for UPSC is structured to test candidates’ understanding of fundamental concepts and their ability to apply them in real-world scenarios. The syllabus covers a wide range of topics spanning various aspects of statics and probability. Here we will analyse the syllabus of Paper 1 and Paper 2 respectively. 

UPSC Statistics Optional Syllabus For  Paper 1 

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 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 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, moment generating function, characteristic function, inversion theorem, Lindenberg and Levy forms of central limit theorem, standard discrete and continuous probability distributions. 
2. Statistical Inference
  • Consistency, unbiasedness, efficiency, sufficiency, completeness, ancillary statistics, 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 Parameter. Estimation by methods of moments, maximum likelihood, least squares, minimum chi square and modified minimum chi square, properties of maximum likelihood and other estimators, asymptotic efficiency, prior and posterior distributions, loss function, risk function, and minimax estimator. Bayes estimators
  • Non-randomised and randomised tests, critical function, MP tests, Neyman-Pearson lemma, UMP tests, monotone likelihood ratio: similar and unbiased tests, UMPU tests for single parameter likelihood ratio test and its asymptotic distribution. Confidence bounds and its relation with tests. 
  • Kolmogorov’s test for goodness of fit and its consistency, sign test and its optimality. Wilcoxon signedranks test and its consistency, Kolmogorov-Smirnov two sample test, run test, Wilcoxon-MannWhitney test and median test, their consistency and asymptotic normality. 
  • 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. 
3. 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 oneway, two-way and three-way classified data, regression analysis, linear regression, curvilinear regression and orthogonal polynomials, multiple regression, multiple and partial correlations, estimation of variance and covariance components, multivariate normal distribution, Mahalanobis’s D2 and Hotelling’s T2 statistics and their applications and properties, discriminant analysis, canonical correlations, 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, probability sampling designs, simple random sampling with and without replacement, stratified random sampling, systematic sampling and its efficacy, 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 HorvitzThompson estimators, non-negative variance estimation with reference to the HorvitzThompson estimator, non-sampling errors. 
  • Fixed effects model (two-way classification) random and mixed effects models (two-way classification with equal observation per cell), CRD, RBD, LSD and their analyses, incomplete block designs, concepts of orthogonality and balance, BIBD, missing plot technique, factorial experiments and 24 and 32, confounding in factorial experiments, split-plot and simple lattice designs, transformation of data Duncan’s multiple range test.

UPSC Statistics Optional Syllabus For  Paper 2

1. 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 charts, cumulative sum chart. 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-Romin tables
  • Concept of reliability, failure rate and reliability functions, reliability of series and parallel systems and other simple configurations, renewal density and renewal function, Failure models: exponential, Weibull, normal, lognormal. Problems in life testing, censored and truncated experiments for exponential models. 
2. Optimization Techniques
  • Different types of models in Operations Research, their construction and general methods of solution, simulation and Monte-Carlo methods 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 queuing theory, M/MI, M/M/K, G/M/l and M/G/1 queues. 
  • Solution of statistical problems on computers using wellknown statistical software packages like SPSS.
3. Quantitative Economics and Official Statistics
  • Determination of trend, seasonal and cyclical components, Box-Jenkins method, tests for stationary series, ARIMA models and determination of orders of autoregressive and moving average components, fore-casting. Commonly used index numbers – Laspeyre’s, Paasche’s and Fisher’s ideal index numbers, cham-base index number, uses and limitations of index numbers, index number of wholesale prices, consumer price, agricultural production and industrial production, test fot index numbers -proportionality, time-reversal, factor-reversal and circular. 
  • General linear model, ordinary least square and generalized least squares methods of estimation, problem of multi-collinearity, consequences and solutions of multi-collinearity, autocorrelation and its consequences, heteroscedasticity of disturbances and its testing, test for independence of disturbances concept of structure and model for simultaneous equations, problem of identification-rank and order conditions of identifiability, two-stage least sauare 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 limitations, principal publications containing such statistics, various official agencies responsible for data collection and their main functions. 
4. Demography and Psychometry
  • Demographic data from census, registration, NSS other surveys, their limitations. 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, quasi-stable population, techniques in estimation of demographic parameters, 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 and reliability of test scores and its determination, use of factor analysis and path analysis in psychometry.

UPSC Statistical Optional Question Paper

Understanding the pattern and types of questions asked in the UPSC Statistics  optional paper is crucial for effective preparation. The UPSC Statistical Optional Question Paper comprises two sections covering a wide range of statistical concepts and their practical applications. 

Section A focuses on foundational topics such as Descriptive Statistics, Probability and Probability Distributions, and Statistical Inference, testing candidates’ abilities to analyze data and draw meaningful conclusions. 

Section B includes more advanced areas including Multivariate Analysis, Linear Models, Time Series Analysis, and Non-parametric Methods, assessing candidates’ proficiency in applying statistical techniques to complex real-world problems. 

Overall, the paper aims to evaluate candidates’ understanding of statistical principles, their ability to apply statistical methods effectively, and their aptitude for critical analysis and interpretation of data.

UPSC Statistical Optional Previous Year Question Papers

Previous year questions serve as invaluable resources for understanding exam patterns, identifying recurring topics, and gauging the level of difficulty. Solving PYQs helps familiarize candidates with the exam format and enhances their problem-solving skills. We’ll discuss the significance of PYQs and offer tips for incorporating them into your study routine.

UPSC Statistics Optional Previous Year Question Papers
Year UPSC Statistics Optional Question Papers PDF Link
2023 UPSC Statistics Optional Paper 1

UPSC Statistical Optional Paper II

2022 UPSC Statistics Optional Question Paper 1

UPSC Statistics Optional Question Paper 2

2021 UPSC Statistics Optional Question Paper 1

UPSC Statistics Optional Question Paper 2

2020 UPSC Statistics Optional Question Paper 1

UPSC Statistics Optional Question Paper 2

2019 UPSC Statistics Optional Question Paper 1

UPSC Statistics Optional Question Paper 2

2018 UPSC Statistics Optional Question Paper 1

UPSC Statistics Optional Question Paper 2

Selecting the right study materials is crucial for success in Statistical Optional exams. We’ll recommend a curated list of textbooks, reference guides, and supplementary resources tailored to the syllabus requirements. These books cover fundamental concepts, advanced topics, and practice exercises to aid comprehensive preparation.

  • An Introduction to Probability Theory & Mathematical Statistics by V K Rohtagi
  • Introductory Probability and Statistical Applications by Paul Meyer
  • Fundamentals of Statistics (2 Vol.) by A M Goon, M K Gupta and B Dass Gupta
  • Introductory Probability and Statistical Applications by Paul Meyer
  • Sampling Techniques by William G. Cochran
  • Fundamentals of Applied Statistics by S C Gupta and V K Kapoor
  • Quantitative Economics by Hoover
  • Sampling Theory of Surveys with Applications by B. V Sukhatme & B V Sukhatme

Is Statistics Optional a Good Subject for UPSC?

Statistics can be a favorable optional subject for UPSC for individuals with a background or interest in commerce-related fields. It offers scoring potential due to its structured syllabus and the ability to leverage existing knowledge. Candidates who enjoy topics like probability, applied statistics, and quantitative economics may find studying this subject both engaging and rewarding. Although almost every subject has some advantages and disadvantages, let us see the various aspects of Statistics optional subject.

Advantages Disadvantages
  • Less Competition: Statistics is a less popular optional subject compared to others like Public Administration or History. This translates to potentially higher marks due to fewer candidates.
  • Scoring Potential: The syllabus is objective and focuses on concepts and calculations, leading to less subjectivity in marking and a chance to score well with good preparation.
  • Static Syllabus: The syllabus for Statistics Optional changes infrequently, allowing you to rely more on standard reference books and previous years’ papers for preparation.
  • Leveraging Background: If you have a background in Statistics or a related field, choosing it as an optional allows you to capitalize on your existing knowledge and potentially excel.
  • Other Career Opportunities: Opting for statistics can open doors to career opportunities in various sectors such as data analysis, research, economics, finance, and government policymaking. 
  • Specialized Subject: The technical nature of Statistics can be challenging for those without a strong foundation in math and probability.
  • Limited Study Material: Finding comprehensive study materials and mock test papers specifically designed for UPSC Statistics Optional can be difficult.
  • Low Overlap with GS: Unlike some optionals, Statistics has minimal overlap with the General Studies papers, requiring dedicated study time for both sections.
  • Self-Study Intensive: Coaching institutes may not offer specialized support for Statistics Optional, making self-study and potentially finding private tutors more crucial.

Statistical Optional Toppers’ Strategies for UPSC Preparation

Analyzing the strategies of previous toppers can offer valuable insights into effective preparation techniques. Studying the topper copies provides aspirants with a roadmap to success, highlighting the key areas to focus on, time management strategies, and recommended resources.

Statistics Optional Notes for UPSC Preparation

To master the Statistics optional paper, aspirants need access to high-quality study materials and notes. Several resources, including textbooks, online courses, and coaching institutes, offer comprehensive study materials tailored to the UPSC syllabus. Additionally, candidates can benefit from creating their own notes, summarizing key concepts, formulas, and case studies for quick revision.

Preparation Strategy for UPSC Statistics Optional Subject

Preparing for the Statistics optional subject for the UPSC exam requires a structured approach and diligent effort. Here’s a concise preparation strategy:

  • Understand the Syllabus- Begin by thoroughly understanding the UPSC syllabus for Statistics. Divide it into manageable sections and prioritize topics based on your familiarity and the weightage of each topic in previous years’ question papers.
  • Study Material Selection- Choose reliable study materials such as standard textbooks, reference books, and online resources that cover the entire syllabus comprehensively. Some recommended books include NCERT textbooks, Indian Accounting Standards, and reference books by renowned authors in Statistical.
  • Create a Study Plan- Develop a realistic study plan that allocates sufficient time to cover each topic systematically. Include regular revisions, practice sessions, and mock tests in your schedule to reinforce learning and track your progress.
  • Practice Questions- Solve previous years’ question papers and sample papers to familiarize yourself with the exam pattern, question types, and time management. Additionally, attempt mock tests to simulate exam conditions and assess your preparation level.
  • Revision and Consolidation- Regularly revise key concepts, formulas, and case studies to reinforce learning and improve retention. Create concise notes summarizing important points to aid in quick revision before the exam.
  • Seek Guidance- Consider joining coaching institutes or online platforms that offer specialized guidance and resources for Statistics optional preparation. Engage with peers, mentors, and subject matter experts to clarify doubts and gain additional insights.

By following this preparation strategy diligently and staying focused, candidates can enhance their chances of performing well in the Statistics optional subject in the UPSC exam.

Conclusion

Choosing the right optional subject is a significant step towards achieving success in the UPSC examination. Whether opting for Statistics or exploring alternatives like Zoology, thorough preparation, and a deep understanding of the syllabus are essential for cracking the exam. With dedication, strategic planning, and the right resources, aspirants can confidently navigate the UPSC optional and realize their dream of serving the nation.

Must Read
NCERT Notes For UPSC UPSC Daily Current Affairs
UPSC Blogs UPSC Daily Editorials
Daily Current Affairs Quiz Daily Main Answer Writing
UPSC Mains Previous Year Papers UPSC Test Series 2024

 

UPSC Statistics Syllabus FAQs

Yes, Statistical optional can help candidates in Indian Forest services, Indian Statistical Service and other statistical services at state level.

Yes, statistics is considered a scoring optional subject. With a structured preparation strategy and thorough understanding of concepts, candidates can secure high marks in both the optional paper and the overall UPSC examination.

Most of the portion of the statistics optional subject of both exams overlap but it differs in some topics.

It depends on various factors like if you have strong hold on the fundamentals and have grip on syllabus and revising regularly and solving mock tests then you don’t need coachings but if any candidate missing these factors can refer to coachings for additional help.

Statistics is often the least preferred optional subject due to its perceived difficulty level, lack of awareness among candidates, limited availability of study materials and guidance, and the misconception that other subjects offer better scoring potential.
/*
*/

Archive Calendar

Mon Tue Wed Thu Fri Sat Sun
 123
45678910
11121314151617
18192021222324
252627282930  

by month

Need help preparing for UPSC or State PSCs?

Connect with our experts to get free counselling & start preparing

Download October 2024 Current Affairs.   Srijan 2025 Program (Prelims+Mains) !     Current Affairs Plus By Sumit Sir   UPSC Prelims2025 Test Series.    IDMP – Self Study Program 2025.

 

THE MOST
LEARNING PLATFORM

Learn From India's Best Faculty

      

Download October 2024 Current Affairs.   Srijan 2025 Program (Prelims+Mains) !     Current Affairs Plus By Sumit Sir   UPSC Prelims2025 Test Series.    IDMP – Self Study Program 2025.

 

Quick Revise Now !
AVAILABLE FOR DOWNLOAD SOON
UDAAN PRELIMS WALLAH
Comprehensive coverage with a concise format
Integration of PYQ within the booklet
Designed as per recent trends of Prelims questions
हिंदी में भी उपलब्ध
Quick Revise Now !
UDAAN PRELIMS WALLAH
Comprehensive coverage with a concise format
Integration of PYQ within the booklet
Designed as per recent trends of Prelims questions
हिंदी में भी उपलब्ध

<div class="new-fform">







    </div>

    Subscribe our Newsletter
    Sign up now for our exclusive newsletter and be the first to know about our latest Initiatives, Quality Content, and much more.
    *Promise! We won't spam you.
    Yes! I want to Subscribe.