B. Sc. in Statistics With Non-Mathematics CombinationANDHRA UNIVERSITY
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Concept of sequences and series, fundamentals of sets and functions, types of functions; solution of simultaneous linear equations, quadratic equation; progressions- AP, GP, HP; permutations and combinations, Binomial theorem.
Definition and types of matrices, addition, subtraction, scalar multiplication and multiplication of matrices, determinant of matrix, transpose of a matrix, inverse and rank of matrix (3 X 3 case only) solution of simultaneous linear equations by matrix methods- Cramer’s Rule, Gauss Jordan Method, Matrix Inversion.
Elements of differentiation, differential coefficient of algebraic and exponential functions only. Maxima and minima of a function, partial derivatives. Elements of integration, Integration by parts and by substitutions.
Definition of statistics, its applications to various disciplines, scope, limitation and distrust of statistics, primary and secondary data, methods of collection of primary data, sources of secondary data, conduct of statistical inquiry, preparation of questionnaire and schedule, editing of primary and secondary data. Classification and tabulation. Characteristics of ideal classification of data, Frequency distribution, Bivariate table, rules of tabulation, simple and complex tables, single, double, and manifold tables.
Data Presentation: diagrams:- Bar diagrams, two dimensional diagrams, square, rectangle and pie chart. Graphs- Histogram, frequency polygon, frequency curve, ogive, semilog and double log graphs.
Measures of Central tendency: Characteristics of good average, AM, GM, HM, Median and Mode- their merits and demerits, graphical location of median and mode, weighted averages, quartiles, deciles, percentiles.
Measures of dispersion: Characteristics of good measures of dispersion, range, Q.D., SD, M.D, Measures of relative variation, coefficient of variation, Lorenz Curve.
Elementary Mathematics and Descriptive Statistics
Paper-II: Statistical Methods
Attributes- Classification of data- double and manifold class, class frequencies and ultimate class frequencies- Contingency tables-Concept of Association and Independence- Types of association – Consistency of data- Various Measures of Association- Yule’s Coefficient of Colligation.
Importance of moments, central and non-central moments, and their interrelationships, Sheppard’s corrections for moments for grouped data. Measures of skewness based on quartiles and moments and kurtosis based on moments with real life examples.
Probability: Basic concepts in probability—deterministic and random experiments, trail, outcome, sample space, event, and operations of events, mutually exclusive and exhaustive events, and equally likely and favourable outcomes with examples– Classical, statistical and axiomatic definitions – addition and multiplication theorems – conditional probability – Statement of Baye’s theorem – simple examples of their direct applications.
Definitions of random variable – discrete random variable, probability function of a discrete random variable – probability mass function (p.m.f) – continuous random variable – probability density function (p.d.f ) – definition of a distribution function for both discrete and continuous random variable – Concept of mathematical expectation statements of its basic results and some simple problems.
Definition, properties and applications of Bernoulli, Binomial, Poisson, Negative binomial, geometric, Hyper Geometric, Rectangular, Normal, Exponential distributions – Simple problems relating to the above distributions.
Need and meaning of Interpolation, Methods of Interpolation – Graphic method – Finite difference – Binomial expression method – Newton’s and Lagrange’s formula for Interpolation.
Unit – IV
Curve fitting: Principles of lease squares-fitting of straight line, parabola, exponential and logarithmic curves- concept of correlation- Types of correlation- Scatter Diagrams – Karl Pearson’s Correlation Coefficient – Spearman’s rank correlation with repeated ranks – Simple Linear regression – Lines of Regression – Regression Coefficients and their properties.
Paper-III: Statistical Applications-I
Concepts of population, sample, parameter, statistic, sampling distribution of a statistic and its standard error (S.E)- Utility of S.E. of a statistic.
Notation of estimation – Point estimation- Concept of good estimator unbiased ness, consistency, sufficiency and efficiency definitions and examples. Concept of Interval estimation –statement of interval estimates for mean, variance of Normal population.
Tests of significance – concepts of null and alternative hypothesis, level of significance, type-I and type-II errors – power of the test – Large sample tests for proportion(s), mean(s) and Standard deviation – Small sample tests – Using t, F and
Non-parametric tests – their advantages – comparison with parametric tests – measurement Scale – nominal, ordinal, interval and ratio. Test procedures of sign test – Wilcoxon signed rank test , median test and run test for randomness.
Need, definition and limitations of Index numbers – simple and weighted index numbers – Laspyer’s, paasche’s and Fisher Index numbers – Criterion of good index numbers – problems involved in the construction of index numbers – Fisher Index number as an ideal index number – Base shifting and splicing of index numbers. Cost of living index numbers. 20 L
Vital Statistics – Introduction – definition, uses, source of vital statistics – registration method, census method – rates and ratios, crude death rates – age specific death rate, standardized death rates – crude birth rate, age specific fertility rate, general fertility rate, total fertility rate. Gross reproductive rate and net reproductive rate – life table and abridged life tables.
Time series – Notation of time series – components of time series – methods of determination of trend by graphical, semi-averages, least squares and moving average methods- Determination of seasonal indices by simple average –ration to trend methods – ration to moving average – link relatives method. 25L
Statistical process control (SPC): Importance of SPC in industry – Concept of chance and assignable causes of variation, Natural tolerance limits, specification limits, Control Charts for variables (Mean, Range, and S.D) and attribute (p, np and C) Charts with fixed and varying sample size – Interpretation of control charts , process capability index and its uses.