Basic Mathematics and Statistics

Paper Code: 
24CSTT101
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This paper is designed to acquaint the students with the fundamental statistical techniques. To understand the role of statistics for analyzing and interpreting data meaningfully. This paper aims to familiarize the students with the handling of univariate and bivariate data.

 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24CSTT101

Basic Mathematics and Statistics

(Theory)

CO 1: Demonstrate the knowledge about the mathematical functions and operations.

CO 2: Classify the data and prepare various diagrams and graphs.

CO 3: Effectively apply exploratory and descriptive data analysis techniques to gain insights and summarize data patterns.

CO 4: Apply correlation and simple linear regression model to real life examples.

CO 5: Identify the problem and apply appropriate laws of probability and Bayes theorem.

CO 6: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures,

Group Discussion,

Classroom Assignment,

Problem Solving Sessions

 

Learning activities for the students:

Assignments,

Seminar,

Presentation,

Subject based  Activities

Classroom, Quiz,

Assignments,

Class Test,

Individual, Presentation

 

14.00
Unit I: 
Basic Mathematics

Basic concepts of Differentiation and Integration: Product Rule, Quotient Rule, Chain Rule, Ilate Rule. Beta and Gamma Integrals (without proof), Expansions: Binomial, logarithmic and exponential. Matrices: Addition, Multiplication, Subtraction, Inverse. Determinant of a matrix.

 

10.00
Unit II: 
Frequency Distributions and Graphical Presentation of Data

Concepts of a statistical population and sample from a population. Classification of data: quantitative, qualitative, chronological, geographical, discrete, continuous. Presentation of data by tables and by diagrams, frequency distributions for discrete and continuous data, graphical representation of a frequency distribution by histogram, frequency polygon and ogive.

 

12.00
Unit III: 
Descriptive Statistics

Measures of central tendency: Mean, Median and Mode. Partition Values. Measures of dispersion (Absolute and Relative measures): Range, Mean Deviation, Quartile Deviation and standard deviation

12.00
Unit IV: 
Correlation and Regression

Correlation: Types of Correlation, Methods of measuring correlation, Properties of correlation coefficient. Regression: Lines of regression, Properties of regression coefficient (without proof).

12.00
Unit V: 
Probability

Random experiment, sample point and sample space, event, algebra of events, Definition of Probability - classical, relative frequency and axiomatic approaches to probability, merits and demerits of these approaches (only general ideas to be given). Theorem on probability, conditional probability, independent events. Baye’s theorem and its applications.

 

Essential Readings: 

ESSENTIAL READINGS:

  • Goon, A.M., Gupta, M.K. and Dasgupta, B. (1991): Fundamentals of Statistics, Volume I, The World Press Pvt    Ltd, Calcutta
  • Gupta, S.C. and Kapoor,V.K.(2000): Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi.
  • Mood Alexander M., Graybill Frankline and Boes Duane C. (2007): Introduction to Theory of Statistics, Mc Graw Hill & Company Third Edition

SUGGESTED READINGS

  • Sharma, G.C. and Jain, Madhu (2001): Essential Mathematics, Galgotia Publications Pvt Ltd.
  • Yule, G.Udny and Kendall,M.G. (1999): An Introduction to the theory of Statistics,14th Edition.
  • Hooda, R.P. (2002): Introduction to Statistics: Macmillan India Ltd. 1st edition.
  • Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Series.
  • Meyer, P.L. (1970): Introductory Probability and Statistical Application, Addision Wesley.
  • Rohatgi, V.K. and Saleh, A.K. Md. Ehsanes (2001): An Introduction to Probability Theory and Statistics, Second Edition, John Wiley andSons.
  • Bhat,B.R (1981): Modern Probability Theory, New Age Publishers, Third edition,

 e-RESOURCES:

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

 

Academic Year: 
2024-2025
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