UPSC Indian Statistical Service (ISS) Provisional Answer Key 2026 - Statistics Paper I & II Released Download PDF

The Union Public Service Commission (UPSC) conducts the Indian Statistical Service (ISS) examination annually to recruit talented statisticians and economists for the Indian Statistical Service and Indian Economic Service. This is an All India examination for candidates with graduation in Statistics, Mathematics, or Economics. The ISS examination consists of a Written Examination (Prelims and Mains) followed by a Personality Test (Interview). Selected candidates serve in various ministries, departments, and statistical organizations across India, contributing to policy formulation, data analysis, and economic planning. The provisional answer key for Statistics Paper I & II allows candidates to estimate their scores and raise objections if any discrepancies are found. Final appointment is subject to document verification and medical examination.

Important Dates

Vacancy Details (Typical / Indicative)

Note: Actual vacancies vary yearly and are announced in the official notification. Some posts may be reserved for PwBD candidates.

Educational Qualification

For Indian Statistical Service:

• Master's Degree in Statistics/Mathematical Statistics/Applied Statistics from a recognized university, OR
• Bachelor's Degree with Statistics/Mathematical Statistics as a subject with at least 60% marks, OR
• Bachelor's degree in Mathematics with at least 60% marks

For Indian Economic Service:

• Master's Degree in Economics/Applied Economics/Business Economics, OR
• Master's Degree in any subject with Economics as one subject at Bachelor's level

Age Limit

Age as on 1st August of the examination year:

Age Relaxation Table:

Nationality

A candidate must be either:

• A citizen of India, OR
• A subject of Nepal, OR
• A subject of Bhutan, OR
• A Tibetan refugee who came to India before 1st January 1962 with intention of permanent settlement, OR
• A person of Indian origin migrated from Pakistan, Burma, Sri Lanka, East African countries, or Vietnam with intention of permanent settlement

Note: Candidates in categories (2) to (5) must obtain a certificate of eligibility from the Government of India.

How to Apply

1. Visit Official UPSC Website: Go to https://upsconline.nic.in or www.upsc.gov.in
2. Register for Part-I: Click on 'Online Application for Various Examinations of UPSC' and complete Part-I registration with basic details, email ID, and mobile number
3. Note Registration ID: After successful Part-I registration, note down the Registration ID and Password generated
4. Complete Part-II: Login using Registration ID and Password to fill Part-II application form with detailed personal, educational, and category information
5. Upload Documents: Upload scanned photograph (3.5 cm × 4.5 cm, 20-50 KB JPEG), signature (4 cm × 1 cm, 10-20 KB JPEG), and other required documents
6. Pay Application Fee: Pay the requisite fee through online mode (Net Banking/Credit Card/Debit Card) or offline mode (SBI Challan)
7. Submit Application: Review all details carefully and submit the application form
8. Take Printout: Download and take printout of the confirmation page for future reference

Application Fees

Note: All Bank Transaction charges for Online Payment to be borne by the candidate. No fee is required for SC/ST/PwBD/Women candidates.

Selection Stages

1. Preliminary Examination (Stage I): Objective type screening test consisting of two papers - General English (200 marks) and General Economics/General Studies (200 marks). This is qualifying in nature and marks are not counted for final merit. Candidates scoring above the cut-off marks proceed to Mains.

1. Main Examination (Stage II): Descriptive written examination comprising four papers for ISS candidates (Statistics I, II, III, IV - each 200 marks) and four papers for IES candidates (Economics I, II, III, General Studies - each 200 marks). Total marks: 800. Only candidates clearing the Mains cut-off are called for Interview.

1. Personality Test/Interview (Stage III): Face-to-face interview conducted by UPSC Board to assess candidate's personality, suitability for service, awareness of current affairs, analytical abilities, and communication skills. Carries 200 marks. Final merit list is prepared based on combined marks of Mains (800) + Interview (200) = 1000 marks.

1. Document Verification: Candidates provisionally selected after interview must appear for document verification where all original certificates (educational, caste, age proof, etc.) are verified against submitted copies.

1. Medical Examination: Finally selected candidates undergo comprehensive medical examination to ensure physical and mental fitness standards required for the service. Medical unfitness can lead to cancellation of candidature even after final selection.

Preliminary Examination Pattern (Indicative)

Negative Marking: 1/3 mark deducted for each wrong answer in objective type papers.

Note: Prelims is only qualifying in nature. Marks not counted for final merit.

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Main Examination Pattern

For Indian Statistical Service (ISS)

For Indian Economic Service (IES)

Negative Marking: Not applicable in Main examination (descriptive type).

Medium: Candidates can choose Hindi or English as the medium for answering Main papers. Statistics/Economics papers can be attempted in either language.

Syllabus for Indian Statistical Service

Statistics Paper I

• Probability: Random experiments, sample space, events, classical and axiomatic definition, addition and multiplication theorems
• Random Variables: Discrete and continuous random variables, probability mass/density functions, distribution functions
• Standard Distributions: Binomial, Poisson, Geometric, Negative Binomial, Hypergeometric, Uniform, Exponential, Gamma, Beta, Normal distributions
• Moments and Generating Functions: Moments, central moments, moment generating function, cumulant generating function, characteristic function
• Multiple Random Variables: Joint, marginal and conditional distributions, independence, covariance, correlation coefficient
• Probability Inequalities: Chebyshev, Markov inequalities
• Limit Theorems: Weak law of large numbers, Central Limit Theorem
• Sampling Distributions: Chi-square, t, F distributions and their applications

Statistics Paper II

• Statistical Inference: Point estimation, unbiasedness, consistency, sufficiency, completeness, Rao-Blackwell theorem
• Methods of Estimation: Maximum Likelihood Estimation, Method of Moments, Least Squares
• Properties of Estimators: Efficiency, Cramer-Rao lower bound, UMVUE, best estimators
• Interval Estimation: Confidence intervals for parameters of normal, binomial, Poisson distributions
• Testing of Hypotheses: Null and alternative hypotheses, Type I and Type II errors, power function
• Most Powerful Tests: Neyman-Pearson lemma, likelihood ratio tests
• Standard Tests: Tests for means, variances, proportions; Chi-square test for goodness of fit and independence
• Non-parametric Tests: Sign test, Wilcoxon signed rank test, Mann-Whitney U test, run test

Statistics Paper III

• Linear Models: Theory of linear estimation, Gauss-Markov theorem, normal equations
• Simple and Multiple Linear Regression: Estimation of parameters, properties of estimators, tests of significance, confidence intervals, prediction
• Analysis of Variance: One-way and two-way classification, fixed and random effects models, multiple comparisons
• Experimental Designs: Completely Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (LSD), factorial experiments
• Correlation and Regression: Simple, partial and multiple correlation, rank correlation
• Categorical Data Analysis: Contingency tables, tests of independence and homogeneity

Statistics Paper IV

• Sample Surveys: Principles of sample surveys, simple random sampling with and without replacement
• Stratified Sampling: Allocation problems - proportional, optimal (Neyman) allocation
• Systematic Sampling: Linear and circular systematic sampling
• Cluster and Multi-stage Sampling: Single and two-stage sampling
• Ratio and Regression Estimators: Bias and MSE, comparison with mean per unit estimator
• Time Series Analysis: Components of time series, trend, seasonal and cyclical variations, smoothing techniques
• Index Numbers: Price and quantity indices, Laspeyre's, Paasche's, Fisher's indices
• Stochastic Processes: Markov chains, random walk, Poisson process, birth and death process
• Statistical Quality Control: Control charts for variables and attributes, acceptance sampling
• Basic Concepts: Official statistics, vital statistics, demographic methods

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Syllabus for Indian Economic Service

Economics Paper I

• Microeconomics: Theory of consumer behaviour, utility maximization, demand theory, production and cost functions
• Market Structure: Perfect competition, monopoly, monopolistic competition, oligopoly
• General Equilibrium: Welfare economics, Pareto optimality, social welfare functions
• Game Theory: Strategic behaviour, Nash equilibrium, cooperative and non-cooperative games
• Information Economics: Asymmetric information, adverse selection, moral hazard, signaling
• Public Economics: Public goods, externalities, taxation, public expenditure

Economics Paper II

• Macroeconomics: National income accounting, Classical and Keynesian models, IS-LM framework
• Consumption and Investment: Consumption theories, investment functions, multiplier-accelerator models
• Money and Banking: Demand for money, money supply, monetary policy, banking system
• Inflation and Unemployment: Phillips curve, NAIRU, inflation dynamics
• Growth Models: Solow model, endogenous growth theory, technical progress
• Open Economy Macroeconomics: Balance of Payments, exchange rate determination, Mundell-Fleming model

Economics Paper III

• Quantitative Economics: Mathematical methods in economics, optimization techniques
• Statistical Methods: Probability, sampling, hypothesis testing, regression analysis
• Econometrics: OLS estimation, violations of classical assumptions, instrumental variables
• Linear Programming: Formulation, graphical and simplex methods, duality
• Input-Output Analysis: Leontief models, applications
• Development Economics: Theories of development, poverty measurement, inequality
• Indian Economy: Economic planning, agriculture, industry, infrastructure, financial sector reforms

General Studies Paper

• Current Affairs: National and international importance, socio-economic developments
• Indian Polity: Constitution, governance, political system, public policy
• Geography: Physical and economic geography of India and world
• History: Modern Indian history, freedom struggle, post-independence developments
• Science and Technology: Developments in science and technology, IT, space, defence
• Environment and Ecology: Climate change, biodiversity, sustainable development

Salary Structure (Typical / Indicative - 7th Pay Commission)

Additional Benefits:

• Medical facilities for self and dependents through CGHS
• Leave Travel Concession (LTC) once in two years
• Pension benefits under National Pension Scheme (NPS) with 14% employer contribution
• Residential accommodation or HRA
• Children Education Allowance (₹2,250 per child, max 2 children)
• Annual Increment (3% of Basic Pay)
• Performance Related Incentive Scheme (PRIS) bonuses
• Study leave provisions for higher studies

Note: Figures are indicative and subject to government revisions. Actual salary depends on posting location, experience, and allowances applicable.

ISS and IES officers follow a well-defined promotion hierarchy with regular career progression. Officers start at Junior Time Scale (Level 10) and can progress through Senior Time Scale (Level 11), Junior Administrative Grade (Level 12), Selection Grade (Level 13), Super Time Scale (Level 14), to apex scales reaching Level 15-16. Promotion is based on seniority-cum-merit, Annual Confidential Reports (ACRs), and departmental promotion committees. Officers can reach positions like Director, Joint Secretary, Additional Secretary, and even Secretary level in various ministries and departments dealing with statistics, economics, and planning.

UPSC releases admit cards for ISS/IES examinations approximately 3 weeks before the scheduled exam date on its official website (https://upsconline.nic.in). Candidates must login using their Registration ID and Password or Date of Birth to download their e-admit card. The admit card contains important details including candidate's name, roll number, exam centre address, reporting time, and exam day instructions. No physical admit card is sent by post. Candidates must bring a printout of the admit card along with original photo ID proof (Aadhaar/Voter ID/Driving License/PAN Card) to the examination centre for verification.

UPSC declares results in multiple stages - Prelims result (usually within 6-8 weeks of examination), Mains result (within 8-10 weeks of Mains examination), and Final result after Interview (within 4-6 weeks of completion of all interviews). Results are published on UPSC's official website with roll numbers of qualified candidates. Detailed marks of individual candidates are made available in the 'Marks' section after final result declaration. Score cards can be downloaded from the website. UPSC does not send individual communication regarding results. Candidates are advised to regularly check the official website for updates and detailed scorecards showing subject-wise and stage-wise marks.

ISS/IES cut-off marks vary significantly based on exam difficulty, number of vacancies, and candidate performance. Typically, General category candidates need to score around 100-120 marks (out of 400) in Prelims to qualify for Mains, while OBC candidates require 90-110 marks and SC/ST candidates need 80-100 marks. For final selection after Mains and Interview (out of 1000 marks), General category cut-off ranges from 450-550 marks, OBC from 420-500 marks, and SC/ST from 380-450 marks. Cut-offs are announced separately for ISS and IES with ISS generally having slightly higher cut-offs. Yearly variations of ±30-50 marks are common based on paper difficulty and vacancy positions.

Examination Centres

UPSC conducts ISS/IES examinations at designated centres across India:

North: Delhi, Chandigarh, Jammu, Shimla, Dehradun, Lucknow, Allahabad, Jaipur

South: Bengaluru, Chennai, Hyderabad, Kochi, Thiruvananthapuram, Madurai, Visakhapatnam, Mysuru

East: Kolkata, Patna, Ranchi, Bhubaneswar, Cuttack, Guwahati

West: Mumbai, Ahmedabad, Pune, Nagpur, Surat, Indore, Bhopal

Northeast: Guwahati, Shillong, Imphal, Agartala, Aizawl, Kohima, Itanagar, Dibrugarh

Central: Delhi NCR, Lucknow, Jaipur, Bhopal, Indore, Raipur

Note: UPSC reserves the right to change exam centres and may add or withdraw centres based on administrative requirements and number of candidates. Candidates are allotted centres based on their preference, subject to availability. Remote candidates from certain regions may get additional travel allowance as per UPSC rules.