STATISTICS (PASS / ELECTIVE)

COURSES OF STUDIES
For
2014 -2015
Admission Batch
BACHELOR OF ARTS
AND
BACHELOR OF SCIENCE
STATISTICS
(PASS / ELECTIVE)
RAVENSHAW UNIVERSITY
CUTTACK
SEMESTER – 1
THEORY
F.M.: 10 + 40
Time – 2 Hours
PAPER – 1 (AE. 1.1.1) and (SP. 1.1.1)
Unit – 1
BASIC MATHEMATICS
Permutation and combination, Binomial theorem, Determinants, Matrices- : Types of matrices,
matrix operations, Rank and Inverse of a matrix.
Limit and Continuity, Differentiation: - differential coefficients from first principle, differential
coefficients of sum, product and quotient, differential coefficient of a function, Integration: Integration by substitution, Integration by parts, definite integral
Unit – 2
STATISTICAL METHODS -1
Idea about types of data, Data Collection, Scrutiny and Analysis of Univariate data.
Frequency distribution, Measures of central tendency, Measures of dispersion, Skewness and
Kurtosis and their measures, Sheppard’s correction for grouped data (without proof)
Theory of curve fitting: Curve fitting by the method of least squares (polynomial, Logarithmic and
Exponential)
Unit – 3
PROBABILITY THEORY
Terminology: trials, events, sample space, mutually exclusive events, exhaustive number of cases,
independent events, equally likely cases, favourable number of cases,
Definition of probability: Classical, Relative Frequency and Axiomatic approach
Probability space, law of addition and law of multiplication of probability, conditional probability
and independence of events, Baye’s theorem and its applications.
2|Page
Random Variables, Mathematical Expectations, Variance and Covariance.
Books Recommended
Santi Narayan
A Text Book of Matrices, S.Chand and Company Ltd.
Santi Narayan
A Text Book of Calculus, S Chand and Company Ltd.
G.Samal
Intermediate Algebra, Vidyapuri
Gupta O.P.
Mathematical Statistics, Kedarnath Ramnath and Co.
Gupta S.C. and Kapoor V.K.
Fundamentals of Mathematical Statistics, Sultan Chand and
Sons
Goon A.N., Gupta M.K. and Dasgupta B.
Fundamentals of Statistics -1, World Press Publication
PRACTICALS
F.M.: 10 + 40
Time – 6 Hours
PAPER – 2 (AE. 1.1.2) and (SP. 1.1.2)
1. Graphical and Diagrammatical presentation of frequency distribution
2. Measures of central tendency and dispersion, their computation interpretation
3. Computation of first four moments for grouped and ungrouped data.
4. Calculation of skewness and kurtosis
5. Fitting of 1st, 2nd, and 3rd degree polynomials, exponential curve. Logarithmic Curve.
SEMESTER – 2
THEORY
F.M.: 10 + 40
Time – 2 Hours
PAPER – 1 (AE. 1.2.3) and (SP. 1.2.3)
3|Page
UNIT – 1 STATISTICAL METHODS -2
Scatter diagram, Correlation and Regression for grouped and ungrouped data, Correlation ratio, Intra
class correlation, Rank correlation
Theory of attributes: Consistency of data, independence and association of attributes, various
measures of association.
Multiple regression, multiple and partial correlation (3 variables only)
Unit – 2
PROBABILITY DISTRIBUTIONS
Binomial, Poisson, Normal and Gamma and Beta distribution (1st and 2nd kind), distribution and
their properties
Unit – 3 FINITE DIFFERENCES
Operators E and ∆, Factorial notations, Separation of symbols, Divided difference, Interpolation with
equal and unequal intervals, Inverse interpolation, Numerical integration ( Trapezoidal rule,
Simpson’s ⅓ rd and ⅜ th rule )
Books Recommended
Gupta O.P.
Mathematical Statistics, Kedarnath Ramnath and Co.
Gupta S.C. and Kapoor V.K.
Fundamentals of Mathematical Statistics, Sultan Chand and
Sons
Goon A.N., Gupta M.K. and Dasgupta B.
Fundamentals of Statistics -1, World Press Publication
PRACTICALS
F.M.: 10 + 40
Time – 6 Hours
PAPER – 4 (AE. 1.2.4) and (SP. 1.2.4)
1. Computation of correlation coefficient for grouped and ungrouped data.
2. Computation of rank correlation coefficient (ties and without ties)
3. Obtaining regression coefficients and regression lines for grouped and ungrouped data.
4. Calculation of multiple and partial correlation and plane of regression (three variables only).
4|Page
5. Coefficient of association for attributes , computation and interpretation
6. Fitting of Binomial, Poisson and Normal distributions
7. Interpolation with equal and unequal intervals
SEMESTER – 3
THEORY
F.M.: 10 + 40
Time – 2 Hours
PAPER – 1 (AE. 2.3.5) and (SP. 2.3.5)
UNIT – 1 TESTS Of SIGNIFICANCE
Concept of population, sample, parameter, null and alternative hypothesis, test of significance, one
tailed and two tailed tests, type 1 and type 2 errors etc. sampling distribution of mean and variance
from normal distribution, large sample theory and large sample tests.
Chi-square distribution and its applications ( test for homogeneity of population variance, test of
goodness of fit and test of independent of attributes)
Small sample theory , t and F distributions , Applications of t and F distributions, Fisher’s Z
transformation, Tests for Sample Correlation Coefficient and Regression Coefficient. ( two variables
only)
UNIT – 2
TIME SERIES, LPP
Time Series :- Definition and Use, Components of Time Series, Measurement of Trend and Seasonal
Component.
Linear Programming Problems ( LPP) : Application and Limitations, Formulation and Solution of
LPP by Graphical Method, Solution of LPP by Simplex Method, Use of Artificial Variables.
UNIT – 3
VITAL STATISTICS
Uses and sources of Vital Statistics, Rates and ratios of Vital Events.
Measurement of Mortality ; - Crude Death Rate, Specific Death Rate, Standardized Death Rate,
Infant Mortality Rate
5|Page
Life Table :- Concept, Assumption, Construction and use, Concept of Stationary and Stable
Population
Measurement of Fertility : - Crude Birth Rate, General Fertility Rate, Specific Fertility Rate, Total
Fertility Rate, Gross Reproduction Rate, Net Reproduction Rate
Books Recommended
Gupta S.C. and Kapoor V.K.
Fundamentals of Mathematica Statistics, Sultan Chand and
Sons
Gupta S.C. and Kapoor V.K.
Fundamentals of Applied Statistics, Sultan Chand and Sons
Goon A.N., Gupta M.K. and Dasgupta B.
S.D.Sharma
Fundamentals of Statistics -II, World Press Publication
Linear Programming Kedarnath Ramnath &co
PRACTICALS
F.M.: 10 + 40
Time – 6 Hours
PAPER – 4 (AE. 2.3.6) and (SP. 2.3.6)
1. Tests based on Chi-square distribution .
2. Tests based on t distribution .
3. Tests based on F distribution.
4. Tests based on Fisher’s Z transformation
5. Determination of Trend and Seasonal Components in Time Series
6. Formulation and Solution of LPP by Graphical Method
7. Solution of LPP by Simplex Method
8. Calculation of Mortality Rates, Fertility Rates and Construction of Life Table
6|Page
SEMESTER – 4
THEORY
F.M.: 10 + 40
Time – 2 Hours
PAPER – 1 (AE. 2.4.7) and (SP. 2.4.5)
UNIT – 1 Design of Experiments
Analysis of Variance (ANOVA) for one way and two way ( one observation per cell) classified data .
Principles of Design of Experiment:- Replication, Randomization and Local Control.
Complete Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (
LSD), and their relative efficiency.
Missing Plot Technique in RBD and LSD ( one missing value)
22 and 23 Factorial Experiments.
UNIT – 2 Design of Sample Surveys
Basic concepts, Important steps in Sample Survey, Principles of Sample Surveys, Sampling and Nonsampling errors, Methods of drawing samples, Types of Sampling Merits and limitations of Sample
Surveys
Simple Random Sampling, Stratified Sampling and Systematic Sampling.
UNIT – 3
INDEX NUMBERS & LPP
Definition, use
and classification of Index Numbers, Important steps in construction of Index
Numbers, Criteria of a good Index Number, Cost of Living Index Number and its construction and
use.
Definition of LPP – formulation of practical problems as LPP, solution of a LPP by graphical method
and simplex method using slack variable (theorems without proof).
7|Page
Books Recommended
Gupta S.C. and Kapoor V.K.
Fundamentals of Applied Statistics, Sultan Chand and Sons
Goon A.N., Gupta M.K. and Dasgupta B.
Fundamentals of Statistics -II, World
PRACTICALS
F.M.: 10 + 40
Time – 6 Hours
PAPER – 4 (AE. 2.4.8) and (SP. 2.4.8)
1. Analysis of CRD, RBD and LSD.
2. Analysis of RBD and LSD with one missing value
2
3
3. Analysis of 2 and 2 Factorial Experiments.
4. Drawing of Simple Random Samples and estimation of Population mean and total with
standard errors.
5. Allocation of Samples in Stratified Random Sampling and estimation of Population mean and
total with standard errors. Comparison of efficiency with Simple Random Sampling
6. Construction of Index Numbers
8|Page

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