Paper VI
BUSINESS STATISTICS
Course Objectives
1.
To familiarise the students with quantitative techniques applicable for business.
2.
To apply the statistical techniques for quantification of data in business.
1.
Introduction - meaning and uses of Statistics in business. (5 hrs.)
2.
Collection and presentation of primary and secondary data - methods of collection - sample and census
- classification and tabulation - frequency distributions - continuous and discrete - line graphs - pie charts -bar
charts - histograms - frequency polygons - ogives - Lorenz curves. (15 hrs.)
3.
Describing Data - measures of central tendency - arithmetic mean - median - mode geometric mean -
harmonic mean - empirical relationship between averages - choice of a suitable average. (15 hrs.)
4.
Measures of Variability - variability - range - mean deviation - standard deviation - variance -
computation of variance and standard deviation - coefficient of variation and its interpretation. (20 hrs.)
5.
Skewness and Kurtosis - introduction - skewness - measures of skewness - Karl Pearson's and Bowleys
coefficient of skewness - test of skewness - kurtosis. (10 hrs.)
6.
Correlation - types - methods of computation - scatter diagrams - correlation graph - coefficient of
correlation
- Karl Pearson's method - Spearman's method - concurrent deviation method - coefficient of determination
-interpretation of 'r' - probable error. (20 hrs.)
7.
Regression Analysis - simple and multiple - dependent and independent variables - regression line -
methods of computation - free hand curve - method of least squares. (15 hrs.)
8.
Time Series - components - measures of trend - method of free hand curve - method of semi-average
-method of moving average - method of least squares. (15 hrs.)
9.
Index Numbers - uses - problems in construction of index numbers - kinds of index numbers - methods
-simple aggregative - simple average of relatives - weighted aggregative - weighted average of relatives -fixed
base and chain base index numbers - consumer price index numbers - methods of construction -precautions. (20
hrs.)
10.
Probability Concepts - approaches to assigning probability - rules of probability - addition rule -
multiplication rule - Bayes' rule - random variable and expected value - probability distributions - binomial
distribution -poisson distribution - normal distribution. (25 hrs.)
Recommended Books
1.
Statistics: Theory, Methods and Application -D.C. Sanchetti and V.K. Kapoor
2.
Stastistical Methods : Dr. S.P. Gupta
3.
Statistics : Theory and Practice - Dr. B.N. Gupta
4.
Fundamentals of Statistics - S.C. Gupta
SECOND SEMESTER EC 202 T - MATHEMATICS - II
Common to B.Sc (Electronics) & B.Sc (Computer Science)
Linear Algebra:
Vector Spaces, Definition and examples, Linear Independence basis, Orthonormal Basis,
Linear transformation, Matrix Via Linear transformation,
. Symmetric, skew symmetric, hermition, and skew hermition matrices, adjoint and inverse of a
matrix, Orthogonal and Unitary matrices, Rank of a matrix, elementary transformations of a
matrix, reduction to normal and echelon form, Consistency and solution of System of linear
equations, characteristic equation of a matrix, Eigen values, Eigen vectors. Cayley Hamilton
theorems, nature of Characteristic roots of diagonal, hermition skew-hermition and unitary
matrices.
Graph Theory
Graph Theory Terminology, Paths and Circuits, Representation of Graphs, Path Matrix,
Adjacency matrix, Exterian paths and circuits, ■Hamiltanian paths and circuits,
Piart HI - Paper I
BUSINESS STATISTICS
Objective
To provide a broad exposure to statistics for business and a few quantitative tools and technics
for application in scientific decision making in business and industry.
UNIT I
1.
. Business Statistics - Introduction - Definitions meaning and
scope - statistics in Govt - statistics in Business and Commerce - Sample Survey - Census and
Sample methods - Law of Statistical regularity and law of inertia of large numbers.
Methods of Sampling - Collection of data classification -tabulation - presentation of data.
2.
Measures of Central tendency - Mean, Median, Mode, W. Arithmetic mean - Different
Positional Numbers Geometric mean - Harmonic mean - Dispersion measures - Skewness
moments - Kurtosis - need in business.
3.
Correlation - Definition - Scope in business scatter diagram Rank Correlation Karl
Pearson's Coefficient of Correlations coefficient (ungrouped data only)
4.
Regression analysis - Meaning - Scope in business Linear and Non Linear Regression
- Dependent and Independent Variables - Lines of best fit and principles of least squares
-Regression equations Regression equation of Y on X'arid X on Y Regression and Correlation.
6
Time Series - Components of. Time Series -Measure of Trend - Method of free hand curve
method of semi Average
- Method of moving average - Method of leas— squares -scope in business.
UNIT If
I. iadsX-Mumheis;* Meaning«Importance problems in constructing index Numbers - Methods
of construction of Index Numbers - Unweighted indices; - Weighted Indices -Computation of
Consumer price index - Cost: of living index - whole sale price index.
InlerppIaiiiM.^ad-.ExtKp.Qiai!fiji; Jniroduction Definition -Meaning - different methods graphic method - Binomial Expansion method - Newton; Advancing difference method
- Lagrange's method.
E.mka!b.ilMy;~ Meaning - Scope in business - Basic Concepts « Frequency approach to
probability classical definition of probability - Axiomatic probability - Addition and
multiplication theorem Permutations and combinations - meaning of nPr and nCr with simple
illustrations - problems based or permutation and combination.
Mairic.ei.MdJ2a£riiliiiajifc Matrices - Definition Scope -order of a matrix - different types of
matrices; - square matrix - row matrix - column matrix - uni matrix, null matrix -Transpose of a
matrix - Matrix; operations - Addition (Subtraction) scalar multiplication and multiplication of
matrices Determinants of order 2 and 3 - Singular matrix minor and co-factor - adjoint of a
matrix * inverse of a matrix -Solution of f linear simultaneous equation; by {1} Using the
Inverse of a matrix (2) Crammer'; rule.
21
THIRD SEMESTER C301T PROBABILITY AND STATISTICS
Module 1 (21 hrs)
Basic statistical concepts, Types of variables, population and sample, Parameter and statistic,
Census versus sampling, Methods of sampling- Random and non random sampling methods.
Frequency distributions- measures of central tendency, measures of dispersion, moments,
skewness and kurtosis.
Correlation and Regression analysis- Types of Correlation, Methods of studying simple
correlation, properties of correlation coefficient.
Module 2(16 hrs)
Different approaches to probability, conditional probability, Addition and multiplication
theorems, Baye's theorem, simple problems.
Random variables and probability distribution- discrete and continuous- distribution function
and its properties(without proof) Extension to bivariate case (elementary concept only)
Module 3(16 hrs)
Expectation and its properties, Mean, variance and moments in terms of expectation, Moment
Generation Function and characteristic function - simple problem, Standard distribution and
statistical inference.
22 Standard probability distribution- Binomial, Poisson, Uniform and Normal- mean, variance
and M.G.F. -problems relating to practical applications.
Module 4(11 hrs)
Central Limit Theorem (without proof) and its applications, Sampling distributions and
standard error(concept only), Distribution of the sample mean, t, X2, and F statistic- definition
and properties (without proof)
Estimation- Concept of Point and Interval estimation-Point estimate and its properties Test of
significance-Elementary ideas and simple problems.
Text Book
Probability and Statistics - Schaum's outline Series.
References
1.
Hogg R.Y- Craig A.L., Introduction to Mathematical Statistica, American Publishing Co.
Pvt. Ltd.
2.
Ltd
Yulg, U.G., Kendoll, M.G; An Introduction to Theory of Statistics, Chailes Griffin & Co.
3.
Draper N.A.,Smith H,; Applied Regression Analysis, John Wiley & Sons, Inc.
4.
S.P. Gupta ^Statistical Methods.
5.
William Mendenhall, Robert J Beaver, Barbara M Beaver, Introduction to Probability and
Statistics, Thomson 2007.
43
FIFTH SEMESTER
C 501 T COMPUTER AIDED OPTIMIZATION TECHNIQUES
Modulel(10 hrs)
Linear Programming: Mathematical formulation, Graphical methods of solution, general
properties, Simplex method, Duality, dual simplex, post-optimality analysis.
Module 2(12 hrs)
Transportation and Assignment Problems: Transportation and transshipment problems,
assignment problems, sample programs.
Module 3(14 hrs)
Network analysis, CPM and PERT: Shorter route problem, maximal flow problem, project
scheduling, critical path calculations, PERT calculations, Sample programs.
Module 4(14 hrs)
Inventory models: Deterministic inventory models, infinite delivery rate with no back orders,
infinite delivery rate with back-orders, finite delivery rate with back orders. Introduction to
probabilistic inventory models, sample programs.
Module 5(14 hrs)
Sequencing models: Processing of n jobs through m2 machines, n jobs through 3 machines, 2
jobs through m machines, maintenance crew scheduling.