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The Indian Statistical Service exam consists of two parts - Part – I and Part – II.

Part I is a written exam carrying a total of 1000 marks in the following 6 subjects for ISS 2015 exam:

A.      Indian Statistical Service

Subjects Marks Time allowed
General English 100 3 Hours
General Studies 100 3 Hours
Statistics I 200 3 Hours
Statistics II 200 3 Hours
Statistics III 200 3 Hours
Statistics IV 200 3 Hours

Part II Viva voce of such candidates as may be called by the Commission, carrying a maximum of 200 marks.

Standard and Syllabi

The standard of papers in General English and General Studies are of a Graduate level studying in Indian University. However, the standards of papers in other subjects would be of Master’s degree level in Indian University in the respective disciplines. Candidates would be expected to illustrate theory by facts and to analyze problems with the help of theory. They must be conversant with Indian problems in the field of Economics.

General English In this paper, a candidate will require to write an essay in English. There would be questions to check the level of understanding of English and workmanlike use of words. Passages will usually be set for precis or summary.

General Studies Here a candidate’s awareness of general knowledge and current happenings would be judged. Candidates should have fair idea about Indian Polity including political system and Constitution of India, Geography and History of India without any special study.

Statistics – I


  • Elements of measure theory
  • Sample Space
  • Class of Events and Probability measure
  • Laws of total and compound probability
  • Bayes’ Theorem
  • Random variables – discrete and continuous
  • Distribution function
  • Moments and cumulants
  • Laws of large numbers and central limit theorems for independent variables
  • Conditional expectation and Martingales

Statistical Methods

  • Collection, compilation and presentation of data
  • Charts, diagrams and histogram
  • Frequency distribution
  • Measures of location, dispersion, skewness and kurtosis
  • Association and Contingency
  • Curve fitting and orthogonal polynomials
  • Distribution of the correlation coefficient, partial and multiple correlation
  • Intraclass correlation
  • Correlation ratio
  • Standard errors and large sample test
  • Non-parametric tests-Goodness of fit, sign, median, run, Wicloxon, Mann-Whitney
  • Rank order statistics-minimum, maximum, range and median
  • Concept of Asymptotic relative efficiency

Numerical Analysis

  • Interpolation formulae (with remainder terms) due to Lagrange, Newton-Gregory, Newton Divided different, Gauss and Striling
  • Euler-Maclaurin’s summation formula
  • Inverse interpolation
  • Numerical integration and differentiation
  • Difference equations of the first order
  • Linear difference equations with constant coefficients

Statistics – II

Linear Models

  • Theory of linear estimation
  • Gauss-Markoff setup
  • Least square estimators
  • Use of g-inverse
  • Tests for regression coefficients


  • Characteristics of good estimator
  • Estimation methods of maximum likelihood
  • Minimum Chi-Square
  • Moments and squares
  • Minimum variance bound estimators
  • Bhattacharya bounds
  • Sufficient estimator
  • Factorization theorem
  • Complete statistics
  • Rao-Blackwell theorem
  • Confidence interval estimation
  • Optimum confidence bounds
  • Resampling, Bootstrap and Jacknife

Hypothesis testing and Statistical Quality Control

  • Hypothesis testing – Simple and composite hypothesis
  • Two kinds of error
  • Critical region
  • Power function
  • Neyman-Pearson fundamental lemma
  • ASN Functions
  • Elements of decision and game theory
  • Statistical quality control
  • Control charts for variable and attributes
  • Acceptance sampling by attributes – Single, double, multiple and sequential Sampling plans
  • Concepts of AOQL and ATI
  • Acceptance Sampling by variables-use of Dodge-Roming and other tables

Multivariate Analysis

  • Multivariate normal distribution
  • Estimation of mean Vector and covariance matrix
  • Mahalanobis’s D2-statistic and their use in testing
  • Wishart’s distribution
  • Wilk’s criterion
  • Discriminant function
  • Principal components
  • Canonical variates and correlations

Statistics – III

Sampling Techniques

  • Census versus sample survey
  • Pilot and large scale sample surveys
  • Role of NSS organization
  • Simple random sampling with and without replacement
  • Stratified sampling and sample allocations
  • Cos and variance functions
  • Ratio and regression methods of estimation
  • Sampling with probability proportional to size
  • Non-sampling errors

Design and Analysis of Experiments

  • Principles of design of experiments
  • Layout and analysis of completely randomized
  • Randomized block and Latin square designs
  • Factorial experiments and confounding in 2n and 3n experiments
  • Split-plot and strip-plot designs
  • Analysis of covariance
  • Analysis of non-orthogonal data
  • Analysis of missing and mixed plot data

Economic Statistics

  • Components of time series
  • Methods of their determination-variate difference method
  • Yule Slutsky effect
  • Correlogram
  • Income distribution-Pareto and Engel curves
  • Concentration curve


  • Theory and analysis of consumer demand-specification and estimation of demand functions
  • Demand elasticities
  • Structure and model
  • Estimation of parameters in single equation model-classical least squares
  • Generalized least-square
  • Heteroscedasticity
  • Serial correlation
  • Rank and other conditions
  • Short-term economic forecasting

Statistics – IV

Stochastic Processes

  • Specifications of a Stochastic Process
  • Markov chains
  • Classification of States
  • Limiting probabilities
  • Stationary distribution
  • Random walk and Gambler’s ruin problem
  • Poisson process
  • Branching process
  • Applications to Queues-M/M1 and M/M/C models

Operations Branch

  • Elements of linear programming
  • Simplex procedure
  • Principal of duality
  • Transport and assignment problems
  • Single and multi-period inventory control models
  • ABC analysis
  • General simulation problems
  • Replacement models for items that fail and or items that deteriorate

Demography and Vital Statistics

  • The life table, its constitution and properties
  • Makehams and Gompertz curves
  • National life tables
  • UN model life tables
  • Abridged life tables
  • Stable and stationary populations
  • Different mortality rates
  • Standardized death rate

Computer Application and Data Processing

  • Computer Application

Computer system concepts: Computer system components and functions, The Central Processing Unit, Main Memory, Bit, Byte, Word, Input/Output Devices, Speeds and memory, capacities in computer systems

Software concepts: Overview of Operating Systems, Types and Functions of Operating System, Application software, Software for multi-tasking, multi-programming, batch processing mode, time sharing mode

Overview of an application specific programme: Flow charts, Basics of Algorithm, Fundamental of design and analysis of Algorithm, Basics of data structure, Queue, Stack

b) Data Processing

Data processing: Digital Number System, Number conversions, Binary representation of integers, Fundamentals of data transmission and processing including error control and error processing

Data base management: Data Resource management. Data base and file organization and processing a) Direct b) Sequential c) Indexed Sequential file. Concepts of Client Server architecture, Data Base Administrator

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