Objective :
To acquaint the students with the basics of Statistics and to introduce to them the utility of statistical techniques in their day-to-day life as well as to cultivate the capabilities to judge and anticipate the trends in trade, commerce, industry and management.
Unit - 1 Correlation and Regression : 16%
Meaning and interpretation of co-efficient of correlation, study of correlation between two variables by scatter diagram. Calculation of r by Karl Pearson's method from grouped and ungrouped data. Rank correlation - Spearman's and Kendal's measures. Probable error and interpretation of r. Coefficient of determination.
Concepts of regression, Principle of least squares, regression lines and regression co-efficient. Use of regression in forecasting.
Unit - 2 Index Numbers : 16%
Meaning and uses; Methods of constructing price and quantity indices - Laspeyre's, Paasche's, Fisher's, Dorbish Bowley's and Marshal - Edgeworth's index numbers, Cost of Living Index Number, Test of adequacy - Time and Factor reversal tests, Chain-base index number; Base shifting and Splicing; Consumer price index number, Problems in constructing index numbers.
Unit - 3 Analysis of Time Series : 17%
Causes of variations in time series data; Components of a time series; Decomposition - Additive and multiplicative models; Determination of trend - Moving averages method and method of least squares (including linear, second degree polynomial, and exponential trend); Computation of seasonal variations by the method of moving averages and seasonal indices by simple averages and ratio-to-moving average methods.
Unit - 4 Matrices and Determinants : 17%
Definition
of a Matrix, Types of matrices - Row, Column, Null, Square, Identity, Diagonal,
Symmetric and Skew-
Symmetric matrix; Transpose of a matrix, Orthogonal matrix; addition subtraction
and multiplication of matrices;
Determinants and third basic properties (without proof); Calculation of Values
of determinants upto third order,
Singular and non-singular matrices; adjoin of a matrix; Finding inverse of a
matrix through adjoin and elementary
row or column operations; Solution of a system of linear equations (for two or
three variables only) simple examples.
Unit - 5 (A) Interpolation and Extrapolation : 10%
Meaning of interpolation & extrapolation; its importance; Methods of interpolation & extrapolation - Newton's method, Binomial expansion method and Lagrange's method.
(B) Forecasting and Methods : 7%
Forecasting - concept, types and importance; General approach to forecasting; Methods of forecasting; Forecasting demand; Industry Vs Company sales forecasts; Factors affecting company sales. Graphical method - Exponential smoothing method.
Unit - 6 (A) Co-ordinate Geometry :
Co-ordinates of a point, slope and intercepts of a line joining two points; equation of a straight line, Different forms of equation of a Straight Line -
(1)
y-y1 x-x1
(3) y= mx + c
-------- = --------
y1-y2
x1-x2
(2) y-y1 = m(x-x1) (4) x + y
-- -- = 1
a b
General equation of a Straight line and its slope and intercepts.
(B) Demographic Methods : 8%
Meaning and scope of demography; Measurements of mortality - Crude death rate, Standardized death rate, Infant mortality rate; Complete life table and its main features, Use of life table; Measurements of fertility - Crude birth rate, general fertility rate, age-specific fertility rate, total fertility rate, gross reproduction rate, net reproduction rate.
Reference Books :
1.
Hooda R.P. : Statistics for Business and Economics; Macmillan, New Delhi.
2. Ya-Lun Chou : Statistical Analysis with Business and Economic Applications,
Holt; Rinehart & Winster, New
York.
3. Levin and Rubin : Statistics of Management, Prentice Hall of India, New
Delhi.
4. Hoel & Jesson : Basic Statistics for Business and Economics; John Wiley
and Sons, New York.
5. N.D. Vohra : Quantitative Techniques in Management; Tata McGraw Hill
Publishing Co. Ltd., New Delhi.
6. R.S.N. Pillai and Mrs V.Bagavathi : Statistics, Sultan Chand & Sons, New
Delhi.
7. Sancheti & Kapoor : Business Statistics, Sultan Chand & Sons, New
Delhi.
8. Sancheti & Kapoor : Business Mathematics; Sultan Chand & Sons, New
Delhi.
9. Srivatava O.S. : A Text Book of Demography, Vikas Publishing.
10. Pressat R. : Statistical Demography, Methuen and Co. Ltd.
Structure of Question Paper (Total Marks - 70, Time : 3 Hours)
1.
The syllabus of the question paper is divided into six units.
2. There must be two questions from each unit which are internally optional.
3. A question paper should be set in such a manner that it covers the whole
syllabus.
4. Each question must carry at least two sub question. Out of these sub
questions at least one should be theoretical and other sub question (s) should
be the example (s).
5. The question paper should give 30% to 35% and 65% to 70% weightage to theory
and examples respectively.
Objective :
To equip the students with advanced knowledge of Statistical techniques used in the study of subjects like Economics, Sociology, Psychology, Agriculture, Commerce, Management, Medicine and other Sciences.
To provide substantial footing in statistics with the view to helping the students in their higher pursuits like C.A., I.C.W.A., C.S., etc.
Unit - 1 & 2 Theory of Sampling : 32%
Simple
Random Sampling with and without replacement; Stratified random Sampling;
Systematic Sampling;
Proof of
(1) (2)
(3)
Derivation of the following formulae:
(1)
(2)
(3) (4)
Proportional and optimum allocations with fixed sample size only. Derivation of the following inequality :
Sampling and non sampling errors.
Unit - 3 Acceptance Sampling : 17%
Sampling inspection plan for attributes; Concepts of AQL, LTPD, Producer's risk and Consumer's risk. OC, AOQ, AOQL, ASN, AOI. Propeties of OC curve for single sampling plan. Single sampling plan for attributes when two points are fixed on the OC curve. Numerical examples for OC, AOQ, ASN and AOI curves of single sampling plan (with C=0 and 1 only) assuming Poisson distribution approximation.
Unit
- 4 Statistical Inference :
(A) Estimation :
8%
Characteristics of a good estimator (only definitions). Estimation of parameters by the Maximum Likelihood Method (Estimation of parameters of Binomial, Poisson and Normal distribution only).
(B) Testing of Statistical Hypothesis : 9%
Simple; Composite; Null and Alternative Hypothesis, Type-I & Type-II errors, Critical Region, Power function and Power of a test. Calculation of the power of a test involving Binomial, Poisson and Normal distributions.
Unit - 5 X2 - test for large samples : 17%
Definition
of X2; Uses of X2 for the following :
(1) Test of goodness of fit (for (Binomial & Poisson Distribution
only)
(2) Test of Independence and Homogeneity in contingency table.
Derivation of X2 for 2 x 2 contingency table and examples for m x n contingency tables. Yate's correction and its application.
Unit - 6 Non-parametric tests : 17%
Idea of non-parametric tests, advantages and disadvantages of non-parametric tests, Sign, Wilcoxon, Mann - Whitney, Median, Run test for one and two samples.
Reference Books :
1.
Sampling techniques : Cochran.
2. Sampling theory and methods : M.N. Murthy.
3. Statistical Quality Control : E.L. Grant.
4. Elements of sampling inspection plans for attributes : S.K. Ekambaram.
5. Fundamentals of Statistics : D.N. Elhance.
6. Introduction to Mathematical Statistics : S.P. Gupta.
7. Statistics : Dr. B.N. Gupta.
8. Fundamentals of Statistics Vol.- I : Goon, Gupta and Dasgupta.
9. Non-parametric Statistics for behavioural Sciences : Siegal S.
10. Statistics for Business and Economics : R.P. Hooda, Macmillan India Limited.
11. Statistics for Management : Levin and Rubin, Prentice Hall of India Pvt.
Ltd., New Delhi.
Structure of Question Paper (Total Marks - 70, Time : 3 Hours)
1.
The syllabus of the question paper is divided into six units.
2. There must be two questions from each unit which are internally optional.
3. A question paper should be set in such a manner that it covers the whole
syllabus.
4. Each question must carry at least two sub question. Out of these sub
questions at least one should be theoretical
and other sub question (s) should be the example (s).
5. The question paper should give 30% to 35% and 65% to 70% weightage to theory
and examples respectively.
Unit - 1 Co-relation and Regression :
Co-relation between two variables, Mathematical definition of r, Proof of the result - 1< r < 1, Effect of change of origin and scale on r, Bivariate table and correlation co-efficient Spearman's rank correlation co-efficient (with proof), Regression between two variables, Derivation of two lines of regression, Properties of Regression Co-efficient (Numerical examples only should be asked in correlation and regression).
Unit - 2 Multiple and Partial Correlation and Regression :
Multiple and partial correlation and regression to be studies for only three variables-plane of regression, Concept of multiple and partial correlation coefficient, Derivation of the formula for b12.3, r12.3 and R1(23) along with the theory. Numerical examples only should be studied.
Unit - 3 & 4 Analysis of Variance & Design of Experiments :
Analysis of Variance for one-way and two-way classifications; Need for design of experiments; fundamental principles of design-randomisation, replication & local control; Lay-out, Construction and analysis of the basic designs - CRD, RBD and LSD. Missing plot techniques with one missing observation in case of RBD and LSD.
Unit - 5 Inventory Control :
Basic functions of inventory and inventory decisions, classical Economic Order Quantity (EOQ) Formulae, Quantity discounts, Relevancy of storage cost, Economic lot size, Buffer Stocks, Buffer stock for variation in demand and in time.
Unit - 6 Simplex Method :
Formulation of Linear Programming Problem, Simplex method (without derivation), artificial basis techniques, degeneracy, revised simplex method, bounded variables techniques, Duality in LP, Statement of duality theorem and application.
Reference Books :
1.
Fundamentals of Statistics : D.N. Elhance.
2. Introduction to Statistics : Weatherburn.
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6. Experimental Design : Cochran & Cox.
7. Fundamentals of Applied Statistics (Sultan Chand) : Gupta and Kapoor.
8. Mathematical Economics : Microeconomic Models (Sultan Chand) : B.C. Mehta.
9. Applied Statistics : (Kapoor Nath, Ram Nath and Co-Meerut) : Ansari, Gupta
and Chaudhary.
10. Statistics for modern business decisions : L.R. Lapin.
11. Quantitative Techniques in Management : N.D. Vohra, Tata McGraw Hill,
Publishing Co. Ltd., New Delhi.
12. Optimization theory and applications : S.S. Rao, New Age International (P)
Ltd., Publishers, New Delhi.
Structure of Question Paper (Total Marks - 70, Time : 3 Hours)
1.
The syllabus of the question paper is divided into six units.
2. There must be two questions from each unit which are internally optional.
3. A question paper should be set in such a manner that it covers the whole
syllabus.
4. Each question must carry at least two sub question. Out of these sub
questions at least one should be theoretical and other sub question (s) should
be the example (s).
5. The question paper should give 30% to 35% and 65% to 70% weightage to theory
and examples respectively.