Statistics Part – I (50 marks)

I. Descriptive Statistics
Definition, Importance and scope of Statistics, 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.

II. 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, Discrete and
Continuous Random Variables, Probability Distribution, Mean and Variance of a
Discrete Probability Distribution.

III. 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

IV. 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
Correlation, Correlation Coefficient, Properties of Correlation Coefficient, Inference
regarding correlation coefficient, Partial Correlation and Multiple Correlation
Coefficients (upto three variables).

V. Non-Parametric Methods
Parametric versus nonparametric tests, when to use non-parametric procedures,
One-sample tests: Sign test, Wilcoxan 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)
I. Sampling & Sampling Distributions
Population and Sample, Advantages of Sampling, Sampling Design, Probability &
Non-Probability Sampling techniques. Brief Concepts of Simple Random, Stratified,
Systematic, Cluster, Multiphase 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.

II. 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 testing for Single Population Proportion and
difference between two population proportions. Estimation of sample size
Analysis of categorized data. Goodness of fit tests. Contingency tables. Test of
independence in contingency tables.

III. 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).

IV. Population Analysis & Vital Statistics
Population and Demographic 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.


Sr. No.TitleAuthor
1.Principles and Procedures of StatisticsSteel, R and Torrie, J.H.
2.Probability and Statistics for Engineers and
Walpole, R.E., Myers, R.H.
and Myers, S.L.
3.Introduction to Statistical Theory, Part-I & IIChaudhry, S.M. and Kamal, S.
4.Introduction to Probability Theory and
Statistical Inference, 3rd Edition.
Larson, H.J.
5.Design and Analysis of ExperimentsMontgomery, D.C.
6.Fundamentals of Modern Statistical
Wilcox, R.
7.Biostatistical AnalysisZar, J.H.
8.Latest Statistical MethodsVaidyanathan, M.
9.Statistical MethodsAggarwal, Y.P.
10.Mathematical StatisticsFreund, John E.
11.Demographic MethodsAndrew Hinde
12.Publications of Federal Board of Statistics
and Provincial Board of Statistics,
Govt. of Pakistan


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