Syllabus (ECONOMICS)

Course Type: MAJ-5

Semester: 4

Course Code: BECOMAJ05T

Course Title: Statistics -I

(L-P-Tu): 5-0-1

Credit: 6

Practical/Theory: Theory

Course Objective:

Learning Outcome: Course Objective After completion of this course, the learner will be able to apply elementary mathematical techniques required in statistics, and to decide and apply appropriate methods and techniques related to simple bivariate analysis, price index num

GROUP A: ELEMENTARY MATHEMATICS FOR STATISTICS (40)

Unit 1: Set Theory (5)

1. Concept, Roster Method and Rule Method, Finite and Infinite Sets, Universal Set, Null Set, Subset & Superset, Complementary Set, Power Set;
2. Union, Intersection, and Subtraction of sets

(c )Venn Diagram, Laws of Set Operations (to be explained using only Venn Diagrams)

(d )Cardinality of Union of two and three sets (no algebraic proof is required, only concept using Venn Diagram) and simple applications

Unit 2: Elementary Algebra (12)

2.1 Permutations and Combinations (5)

(a) Concepts and elementary applications only

(b) Use of calculator

2.2: Binomial Theorem (2)

Expansion of (a+b)ⁿ where n is a positive integer, finding a particular term or its coefficient in the expansion, Relations of combinations obtained using Binomial Theorem (no proof is required throughout)

2.3: Exponential Function (1)

1. Introduction to e, functions in the form e^x, e^-x, e^1/x and their graphs (first quadrant only);

(b)Use of Calculator

2.4: Logarithm (4)

1. Concept, Rules/Formulas (no proof is required), elementary numeric problems (with emphasis on, but not limited to, base 10 and e), elementary algebraic problems for application of rules/formulas;
2. Concept of anti-logarithm (no application);

(c )Log-table and its use in finding values;

(d )Use of Calculator in finding log and anti-log values.

Unit 3: Elementary concepts from calculus (23)

3.1 Functions (5)

Concept; Domain and Range of a function; Function of a Function; Graph of linear functions (detail); Graph of quadratic and cubic functions (in general, no particular functional form is to be used); introduction to logarithmic and exponential functions (no applications)

3.2 Limit & Continuity (1)

Concept; Existence of Limit; neither formulas nor applications

3.3 Differentiation (10)

(a) Concept; Existence; First Principle (no proofs/sums), formula of differentiation of only algebraic, exponential, and logarithmic functions (with elementary sums); differentiation of the sum, product, and ratio of functions (with elementary sums); introduction to chain rule and applications (up to multiplication of two derivatives)

(b) Introduction to and elementary sums on Double Differentiation

(c )Differentiation of functions of more than one independent variable – Introduction to and elementary sums on Partial Differentiation and Total Differentiation

(d )Concept of Maxima and Minima of functions of only one independent variable, and their conditions (no applications)

3.4 Integration (7)

Concept; basic formulas (only algebraic and exponential) and their elementary applications; method of substitution; integration by parts, concept of definite integral as area under a curve; simple applications (no formula involving logarithmic or trigonometric expressions are required throughout)

GROUP B: STATISTICS (50)

Unit 1: Elementary Statistics (10)

Axioms of Central Tendency; Theory of Dispersion; Skewness and Kurtosis; Mathematical Problems on Mean, Median, Mode, Range, Mean Deviation, Standard Deviation, Coefficient of Variation.

Unit 2: Bivariate Analysis (20)

1. Why study this unit, real life problems which can be answered after studying this unit; Bivariate data – concept, Scatter Diagram – Definition, Uses (2)
2. Pearson’s Correlation Coefficient (5)

(c )Simple Linear Regression – Concept, Derivation of Regression Equations using the Method of Least Squares (normal equations are to be derived using calculus, estimated parameters must be denoted using hats), Applications, Relation between Total Variation, Explained Variation, and Unexplained Variation (with proof), introduction to coefficient of determination (r²) – Determination of angle between two regression lines is not required (10)

(d ) Spearman’s Rank Correlation (both non-tied and tied cases) (3)

Unit 3: Index Number (20)

1. Why study this unit, real life problems which can be answered after studying this unit; Price Index Number – Concept, Definition, Uses. (6)
2. Aggregative and Relatives methods of calculating Price Index Numbers (Simple and Weighted Average of Price Relatives, Simple Aggregative Method, Weighted Aggregative Methods – Laspeyres, Paasche, Fisher, Marshall-Edgeworth), Tests for an ideal price index number (10)

(c) Chain Base Index Numbers vs. Fixed Base Index Numbers, Introduction to Quantity Index Number (only concept, no applications) (2)

(d) Cost of Living Index number – Concept, Uses, and Applications – Dearness Allowance, Real Wage, Real GDP (2)

Reading References:

Group A: Elementary Mathematics for Statistics

1. Relevant parts from the NCERT Class XI & XII Mathematics Books (OER).
2. Sanjay Mishra, 2021, Fundamentals of Mathematics, 2^nd edition, GK Publication.
3. Garima Singh, 2020, Mathematics (Volume I and II), AICTE Prescribed Textbook, Khanna Book Publishing Co. Ltd.
4. BC Das and BN Mukherjee, 1994, Integral Calculus Including Differential Equations, UN Dhar & Sons Private Ltd.
5. Arup Mukherjee, 2004, Linear Programming and Numerical Analysis, Shreetara Prakashani, Kolkata.

Group B: Statistics

1. Goon, A. M., Gupta, M. K., & Dasgupta, B., 2013, Fundamentals of Statistics (Volume I and II), The World Press Private Ltd.
2. NG Das, 2017, Statistical Methods (Combined Volume), McGraw Hill Education, Kolkata.
3. R.V. Hogg and A.T. Craig, An Introduction to Mathematical Statistics, Third Edition, Amerind, New York, London.
4. Mood, A.M., F.A. Greybill and D.C. Boes, 1974, Introduction to the Theory of Statistics, McGraw Hill.
5. John E. Freund, 1992, Mathematical Statistics, Prentice Hall.
6. R. Ganesan and PV Sreenivasaiah, 2015, Textbook of Statistics, Write and Print Publication, 1^st edition.
7. SS Gupta and VK Kapoor, 2020, Fundamentals of Mathematical Statistics, 12^th edition, Sultan Chand & Sons.