Road Maps

Statistics

100 marks · 1 paper · 180 minutes per paper

0%Complete

Preparation duration is an estimate and may vary according to your academic background, available study time and familiarity with the subject.

Stage 1Orientation

Understand the official syllabus, paper structure, marks and preparation resources.

Read and annotate the official FPSC syllabusReview every paper, section, marks allocation and official instruction before beginning preparation.

Set up subject resourcesCreate folders or notebooks for syllabus notes, practice, past papers and revision material.

Review the paper formatUnderstand the number of papers, marks, duration and relevant language or MCQ rules.

Stage 2Foundation

Build the concepts, terminology and prerequisite knowledge needed for the subject.

Build a subject glossaryList and define the core terminology needed across the syllabus.

Map prerequisite conceptsIdentify foundational concepts and arrange them before advanced topics.

Stage 3Official Syllabus Coverage

Cover every official FPSC topic in a practical sequence.

Cover: Subject overviewStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: PAPER: STATISTICS (100 MARKS) Part – I (50 marks)

Cover: Descriptive StatisticsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Definition, Importance and scope of Statistic s, Descriptive and Inferential Statistics, Presentation of the Data, Tables, Graphs and Charts: Stem -and leaf diagram, Box and Whisker Plots. Measures of Central Tendency/location, Measures of Dispersion/Variability: Measures of Skewness and Kurtosis.

Cover: Basic ProbabilityStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Basic Probability Concepts, Additive and Multiplicative laws of Probability, Joint and Marginal Probabilities, Conditional Probability and Statistical Independence, Bayes’ rule. Concept of a Random Variable, Mathematical Expectations, Discret e and Continuous Random Variables, Probability Distribution, Mean and Varian ce of a Discrete Probability Distribution.

Cover: Probability DistributionsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Discrete and continuous Probability Distributions. Properties, applications of Binomial, Poisson, Hyper -geometric distribution, Normal Distribution and its properties, Standard Normal Curve, Normal approximation to Binomial and Poisson distribution.

Cover: Regression Analysis & Correlation AnalysisStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Concepts of Regression and Correlation and their application, Simple and Multiple Linear Regression (upto three variables) , Estimation of the Parameters of simple regression Model , Method of least square, Inference regarding regression parameters. Correlation, Correlation Coefficient, Properties of Correlation Coefficient, Infe rence regarding correlation coefficient , Partial Correlation and Multiple Correlation Coefficients (upto three variables).

Cover: Non-Parametric MethodsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Parametric versus nonparametric tests, when to use non -parametric procedures, One-sample tests: Sign test, Wil coxan signed ranks tests, Kolmogrov -Smirnov test, run test. Tests for two related samples: sign test, run tests, chi -square test, Test for two independent samples: Mann-Whitney test, Kolmogrov-Smirnov test. Part – II (50 marks)

Cover: Sampling & Sampling DistributionsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Population and Sample, Advantages of Sampling, Sampling Design, Probability & Non-Probability Sampling techniques. Brief Concepts of Simple Random, Stratified, Systematic, Cluster, Multip hase and Multistage Sampling. Non-probability sampling: Purposive, Quota Sampling, Convenience & Accidental Sampling. Sampling with and without replacement, Application of Central Limit Theorem in Sampling, Sampling Distribution of Mean, difference between two Means, Proportion, difference between two Proportion and Variance.

Cover: Statistical InferencesStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Estimation: Point Estimation, Properties of a good Estimator. Interval Estimation. Interval Estimation of Single Population means and Single proportion . Difference between two means and Difference between two proportions. Hypothesis Testing: Types of errors. Hypothesis Testing for Population Mean. Inferences for difference between Two Population Means. Inferences for the difference between Means of Two Normal Populations using Independent Samples (variances are assumed Equal) for sample size. Inference for Two Populations Mean using Paired Samples. Hypothesis tes ting for Single Population Proportion and difference between two population proportions. Estimation of sample size Analysis of categorized data. Goodness of fit test s. Contingency tables. Test of independence in contingency tabl

Cover: Design of ExperimentsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: One-way and Two -way Analysis of Variance, Design of Experiments, Concepts of Treatment, Replication, Blocking, Experimental Units and Experimental Error, Basic Principles of Design of Experiments, Description, Layout and Statistical Analysis of Completely Randomized Design (CRD), Randomized Complete Block Design (RCBD), Multiple Comparison tests (LSD test).

Cover: Population Analysis & Vital StatisticsStudy the official syllabus content, prepare notes, identify likely examination angles and mark weak areas. Official scope: Population and Demograp hic Methods, Sources of Demographic data, Basic Demographic Measures, Sex Ratio, Child Women Ratio, Vital Index, Crude and Specific Birth and Death Rates, Total Fertility and Net Reproduction Rates. Official Statistics: Statistical Systems in Pakistan, Functions of Statistics Division , Bureaus of Statistics and NADRA. The National Income, Gross Domestic Product, Saving and Wealth, Index Numbers.

Stage 4Consolidation

Prepare short notes, comparisons, evidence, diagrams, facts, formulas or timelines.

Prepare concise revision notesCompress covered material into quick revision notes without removing required syllabus coverage.

Create connections and comparison materialUse tables, diagrams, timelines, formulas, maps or concept links where suitable for this subject.

Stage 5Exam Application

Apply knowledge through the paper-specific practice format.

Create a formula, definition or methods sheetComplete this task under exam-oriented conditions and record areas that need revision.

Solve worked examples and numerical/problem setsComplete this task under exam-oriented conditions and record areas that need revision.

Attempt a timed technical question setComplete this task under exam-oriented conditions and record areas that need revision.

Stage 6Past Papers

Attempt topic-wise and full-length past-paper practice.

Classify past-paper questions by syllabus topicUse validated official past papers and link each question to the relevant syllabus topic.

Attempt a timed past paperAttempt a complete paper or equivalent question set within the official time limit.

Stage 7Revision and Mock Examination

Complete layered revision, weak-area review and a timed mock paper.

Complete first revisionReview all notes and update topics marked Needs Revision.

Complete second revisionFocus on recall, structure, evidence, formulas or language accuracy.

Attempt final mock examinationComplete a timed mock and evaluate coverage, accuracy, structure and time management.

Paper 1 · 100 marks

Subject overview

PAPER: STATISTICS (100 MARKS) Part – I (50 marks)

Descriptive Statistics

Definition, Importance and scope of Statistic s, Descriptive and Inferential Statistics, Presentation of the Data, Tables, Graphs and Charts: Stem -and leaf diagram, Box and Whisker Plots. Measures of Central Tendency/location, Measures of Dispersion/Variability: Measures of Skewness and Kurtosis.

Basic Probability

Basic Probability Concepts, Additive and Multiplicative laws of Probability, Joint and Marginal Probabilities, Conditional Probability and Statistical Independence, Bayes’ rule. Concept of a Random Variable, Mathematical Expectations, Discret e and Continuous Random Variables, Probability Distribution, Mean and Varian ce of a Discrete Probability Distribution.

Probability Distributions

Discrete and continuous Probability Distributions. Properties, applications of Binomial, Poisson, Hyper -geometric distribution, Normal Distribution and its properties, Standard Normal Curve, Normal approximation to Binomial and Poisson distribution.

Regression Analysis & Correlation Analysis

Concepts of Regression and Correlation and their application, Simple and Multiple Linear Regression (upto three variables) , Estimation of the Parameters of simple regression Model , Method of least square, Inference regarding regression parameters. Correlation, Correlation Coefficient, Properties of Correlation Coefficient, Infe rence regarding correlation coefficient , Partial Correlation and Multiple Correlation Coefficients (upto three variables).

Non-Parametric Methods

Parametric versus nonparametric tests, when to use non -parametric procedures, One-sample tests: Sign test, Wil coxan signed ranks tests, Kolmogrov -Smirnov test, run test. Tests for two related samples: sign test, run tests, chi -square test, Test for two independent samples: Mann-Whitney test, Kolmogrov-Smirnov test. Part – II (50 marks)

Sampling & Sampling Distributions

Population and Sample, Advantages of Sampling, Sampling Design, Probability & Non-Probability Sampling techniques. Brief Concepts of Simple Random, Stratified, Systematic, Cluster, Multip hase and Multistage Sampling. Non-probability sampling: Purposive, Quota Sampling, Convenience & Accidental Sampling. Sampling with and without replacement, Application of Central Limit Theorem in Sampling, Sampling Distribution of Mean, difference between two Means, Proportion, difference between two Proportion and Variance.

Statistical Inferences

Estimation: Point Estimation, Properties of a good Estimator. Interval Estimation. Interval Estimation of Single Population means and Single proportion . Difference between two means and Difference between two proportions. Hypothesis Testing: Types of errors. Hypothesis Testing for Population Mean. Inferences for difference between Two Population Means. Inferences for the difference between Means of Two Normal Populations using Independent Samples (variances are assumed Equal) for sample size. Inference for Two Populations Mean using Paired Samples. Hypothesis tes ting for Single Population Proportion and difference between two population proportions. Estimation of sample size Analysis of categorized data. Goodness of fit test s. Contingency tables. Test of independence in contingency tables.

Design of Experiments

One-way and Two -way Analysis of Variance, Design of Experiments, Concepts of Treatment, Replication, Blocking, Experimental Units and Experimental Error, Basic Principles of Design of Experiments, Description, Layout and Statistical Analysis of Completely Randomized Design (CRD), Randomized Complete Block Design (RCBD), Multiple Comparison tests (LSD test).

Population Analysis & Vital Statistics

Population and Demograp hic Methods, Sources of Demographic data, Basic Demographic Measures, Sex Ratio, Child Women Ratio, Vital Index, Crude and Specific Birth and Death Rates, Total Fertility and Net Reproduction Rates. Official Statistics: Statistical Systems in Pakistan, Functions of Statistics Division , Bureaus of Statistics and NADRA. The National Income, Gross Domestic Product, Saving and Wealth, Index Numbers.

Suggested ReadingsSr. No. Title Author
Suggested ReadingsPrinciples and Procedures of Statistics Steel, R and Torrie, J.H.
Suggested ReadingsProbability and Statistics for Engineers and Scientist Walpole, R.E., Myers, R.H. and Myers, S.L.
Suggested ReadingsIntroduction to Statistical Theory, Part-I & II Chaudhry, S.M. and Kamal, S.
Suggested ReadingsIntroduction to Probability Theory and Statistical Inference, 3rd Edition. Larson, H.J.
Suggested ReadingsDesign and Analysis of Experiments Montgomery, D.C.
Suggested ReadingsFundamentals of Modern Statistical Methods Wilcox, R.
Suggested ReadingsBiostatistical Analysis Zar, J.H.
Suggested ReadingsLatest Statistical Methods Vaidyanathan, M.
Suggested ReadingsStatistical Methods Aggarwal, Y.P.
Suggested ReadingsMathematical Statistics Freund, John E.
Suggested ReadingsDemographic Methods Andrew Hinde
Suggested ReadingsPublications of Federal Board of Statistics and Provincial Board of Statistics, Pakistan. Govt. of Pakistan

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