Syllabus of basic statistics - Delhi university

BASIC STATISTICS

Course Objectives:

(i) The scope of Statistics has been well recognized over the years but has very
much expanded in the recent years and with the impressive progress in
Computers and research, significant applications to Social Sciences have ever
been on increase. The objective is to give basic knowledge of the subject and
familiarity with techniques to use them effectively. Knowledge of Mathematics
at Senior Secondary level will be and advantage but not necessary for offering
this course.
(ii) Due to the special nature of the course, students offering Discipline courses in
Statistics will not be permitted to offer this application course. Also the
medium of instruction for the course will be English.
(iii) The usual lecture, Tutorial and Assignments will be supplemented with
supervised reading and problem sessions, online lessons, websites, films and
computer software aided learning. Laboratory Work / Practicals and Projects
highlighting applications to various Social sciences as per the interest of the
individual student and advice of the teacher will be a significant part of each of
the course as per details specified in the course. Central Science Library
receives periodicals containing regular information on such materials and
standard books by many reputed publishers and software packages by agencies
like Springer Verlag, Wiley Interscience, Prentice Hall , American
Mathematical Society, SPSS South Asia (for instance, http://www.ams.org.
and www.spss.co.in).
(iv) Guidelines for the conduct of the courses will be prepared and circulated to the
colleges and Examination Branch well in time and updated regularly.
Combined Three-week Refresher Course(s) for all the course for teachers
will be conducted during the next two academic years. Emphasis will be on the
effective Methods of teaching /Laboratory Work / Practicals and Projects
highlighting applications to various Social Sciences. Preparation of,
Information on and regular update of the Supplementary Reading / online
materials and projects will be undertaken during the next two academic years.
Notes:
(i) The course is divided roughly into three units to be taught with 5 Lectures and
two hours for Practical / Laboratory / Project Work per week and provision for
Tutorials as per University rules.
(ii) Every student has to do a project related to actual data and learn how to use
available software.
(iii) Fifty-five marks will be reserved for the final two-hour written examination.
(iv) Twenty marks will be reserved for the Internal Assessment as per University
rules.
(v) Twenty-five marks will be reserved for the Practical / Laboratory / Project Work
examination comprising of Laboratory and Project records (five marks each),
examination (ten marks) and viva-voce (five marks).
Syllabus:

Unit 1. FUNDAMENTALS OF DATA ANALYSIS AND PROBABILITY
THEORY

Collection and Presentation of Data
Meaning and Scope of Statistics.
Collection of Statistical Data : Census and Sample survey.
Types of Data : Primary and Secondary, Cross-section and Time Series, Univariate and
Bivariate.
Graphical Presentation of Data : Pie charts and Bar graphs, Frequency distribution,
Histograms and Ogives. Bivariate frequency distribution.
Descriptive Summary Measures of Univariate Data
Measures of Central Tendency: Mean, Median and Mode.
Measures of Dispersion: Range, Quartile Deviation, Mean Deviation, Standard
Deviation, Coefficient of variation, Deciles and Percentiles.
Coefficients of Skewness and Kurtosis.
Statistical Moments: Central and Non-central.
Descriptive Analysis of Bivariate Data
Methods and measures of studying relationship between two variables : Scatter
Diagrams, Simple correlation coefficient, Rank correlation coefficient, Linear
Regression, Coefficient of determination.
Estimation of simple and exponential trends for Time Series.
Elements of Probability Theory
Random experiments, Sample Space and events.
Different Approaches to Probability : Classical, Frequency interpretation and Axiomatic
approach, Deduction of simple properties from axioms.Counting techniques and their use
in Probability.Conditional Probability : Independence of Events, Bayes’ Theorem and its
applications.

Unit 2. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS

Discrete Random Variable, Probability Distribution and Mathematical Expectation
Meaning of a random variable, Probability Distribution of a random variable,
Distribution function.
Binomial and Poisson distributions.
Mathematical Expectation and variance.
Joint and Marginal distributions.
Independence of random variables.
Continuous Random Variable
Probability density function, Distribution function, Mathematical expectation and
variance.
Uniform distribution. Exponential distribution.
Normal Distribution and Limit Theorems
Normal Distribution, its properties and importance.
Weak Law of large numbers. Interpretation of Central Limit Theorem.

Unit 3. SAMPLING AND STATISTICAL INFERENCE

Sampling Distributions
Random sample, Parameter and Statistic.
Sampling distribution of a statistic.
Distributions of sample mean, sample variance and sample proportion.
Introduction to chi-square, Student’s t- and F- distributions.
Estimation of Parameters
Problem of Point estimation.
Unbiasedness and efficiency of estimators.
Estimators for population mean, variance and proportion.
Interval Estimation: Confidence intervals.
Confidence intervals for the mean of a normal population with known or unknown
population variance. Confidence intervals for variance of a normal population.
Confidence intervals for the population proportion and for the difference between two
population proportions.
Testing of Hypothesis
Two types of errors. Level of significance.
Tests for the mean of a normal population with known or unknown population variance
and Test for the difference between two means.
Test for the variance of a normal population.
Tests for the population proportion and for the difference between two population
proportions.

Syllabus of basic statistics - Delhi university

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