GOVERNMENT COLLEGE (A) : RAJAHMUNDRY B.A I Year ...gcrjy.ac.in/departments/syllabus/d9fc5b73a8d78fad3d6dffe419384e… · Practicals- Semester-I Conduct any 6 Practicals. 1. Solution

GOVERNMENT COLLEGE (A) : RAJAHMUNDRY

B.A I Year: Statistics Syllabus(For Non-Mathematics Combination)

Semester-I CBCSModule 1: Elementary Mathematics(Without Mathematical Derivations)

Total Hrs per Week:04 Total Credits: 03-----------------------------------------------------------------------------------------

Unit-1:

Concept of sequences and series, fundamentals of sets and functions, types of functions; solution of simultaneous linear equations, quadratic equations.

Unit-II

progressions- AP,GP, HP; permutations, combinations, Binomial theorem and their related problems.

Unit-III

Elementary Matrices: Definition and types of matrices, addition, subtraction, scalar multiplication of matrices.

Unit-IV

Determinant of matrix,Transpose of a matrix, inverse and rank of 3 X 3 matrices only. Solution of simultaneous linear equations by matrix methods- Cramer’s Rule and MatrixInversion methods.

Unit-VDifferentiations: Derivatives of algebraic and exponential functions.. Maxima and minima of a function. Integration basics, Integration by parts and by substitutions.

TEXT BOOKS

1. Differential Calculus- Santhi Narayana.2. Outlines of Matrices-Schaum.

Reference Books:

1)S.P.Gupta: Statistical Methods. Sultan Chand2)S.C.Gupta and V.K.Kapur: Fundamentals of Mathematical Statistics. Sultan Chand.3.Moulika Ganithamu Sambavyata - Telugu Academy.4. Quantitative Techniques I- Sultan Chand Publication.

Practicals- Semester-I

Conduct any 6 Practicals.

1. Solution to Simultaneous Linear equations2. Progressions- AP, GP, HP3. Addition, Subtraction, Multiplication of Matrices.4. Determinant of a Matrix5. Solution of equations by Matrix methods.6. Simple differentiation7. Integrations

GOVERNMENT COLLEGE (AUTONOMOUS) RAJAMAHENDRAVARAM

FIRST SEMESTER END EXAMINATIONI BA – STATISTICS (SEMESTER-I)ELEMENTARY MATHEMATICS

Time: 3hrs Max Marks-60MODEL PAPER

SECTION –A5x4=20M

Answer any five of the following.

1. Obtain the roots of the quadratic equation ax2 + bx +c =0ax2 + bx +c =0 అన ేవర? స? కరణా? ిమూల లు క గొ మ .

2. Explain permutation and combination with examples.ప?? లు మ య సం? గ ల ఉదాహరణలత? ?వ ంప మ .

3. Write short notes on Arithmetic progressionణ??య ???? కు?ప?మ గ ?యండ.

4. Define finite set. ప ? స? ?? ?ర??ంప మ

5. nc3 =nc5 find n . nc3 =nc5 అ త n ?లువ ఎం ?

6. Define matrix and its propertiesమ ??క ?ర??ం? దా? ? క? ధ ?ల ?ర??ంచ మ .

7. State and explain Binomial theoremద?ప ద?ాం మ ొ?? ?వ ంప మ .

8. Find the derivative of Y = X2 + 2X + 1.Y = X2 + 2X + 1 ? క? అవకల మ క గొ మ .

SECTION-BAnswer all the questions: 4x8=32M

9a) If A= B= and C=

Prove the following equation

A= B= and C= అ ప ?

?ర ంచండ.

(OR)b) Find the sum and product of the roots of the equation x2+4x +3 = 0

x2+4x +3 = 0 అన ేస? కర ? ి మూల ల ? త?ా?? మ య ఉ ???? క గొ మ .

10a) Find sum of ‘n’ terms of the series 7+77+777+……….7+77+777+………. అన ేసర?ల? n పడాల ? క? ? త?ా?? క గొ మ .

b) Find the 6th term in the expansion of (2x/3 + 3y/9)9

Find the middle term in the expansion of (3x/7 – 2y)10

(2x/3 + 3y/9)9ల? ?స?రణల? 6 వ ప మ క గొ మ .

(3x/7 – 2y)10?స?రణల? మధ? ప మ క గొ మ .

11a)Solve the following equations by cramer method

?ింద స? కరణమ ల ? ? ప ?? దా? ంచ మ .

(OR)b) Solve the following equation s by inverse matrix method

?ింద స? కరణమ ల మ ??క ?ల?మ ప ?? దా? ంచ మ

12a)

If A = then find A-1

(OR)

b) Evaluate

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GOVERNMENT COLLEGE (A) : RAJAHMUNDRY

B.A I Year: Statistics Syllabus(For Non-Mathematics Combination)

Semester-II CBCSModule-2 : Descriptive Statistics

(Without Mathematical Derivations)Total Hrs per week:04 Total Credits:03--------------------------------------------------------------------------------------------Unit-1 : Introduction to Statistics: Statistics, Definition, application, scope, limitation, primary and secondary data, methods of collecting primary and secondary data. Statistical enquiry, questionnaire and schedule, Editing of data.

Unit-II :Classification and tabulation: Classification of data, frequency distribution, rules of tabulation, simple and complex tables, single, double and manifold tables.

Unit-III:Diagrammatic Representation: Bar diagrams, square, rectangle, pie-charts, Histogram, frequency polygon, ogives.

Unit-IV:Measures of Central Tendency: Mean, Median, Mode, G.M & H.M, merits and demerits, finding median by graphic method, quartiles, deciles & percentiles.

Unit-V:Measures of Dispersion: Range, Q.D, S.D, M.D, Coefficient of variation, Lorenzcurve.

Text Books:1. Statistical Methods-S.P.Gupta2. Fundamentals of Mathematical Statistics- SC Gupta and V.K.Kapoor3. 3.Moulika Ganithamu Sambavyata - Telugu Academy.

Reference Books:4. Quantitative Techniques I-Sultan Chand Publication

Practicals- Semester-IIConduct any 6 Practicals.1. Arithmetic Mean, Median, Mode, GM, HM.2. Calculation of CV and its comparisons.3. Bar diagrams4. Pie diagrams5. Histogram6. Frequency and Polygon.7. 7.Ogive curves.

GOVERNMENT COLLEGE (AUTONOMOUS) RAJAMAHENDRAVARAM

FIRST SEMESTER END EXAMINATIONI BA – STATISTICS (SEMESTER-II)

DESCRIPTIVE STATISTICSTime: 3hrs MODEL PAPER Max Marks-60

SECTION_A

Answer any five of the following. All questions carry equal marks. 5 x 4 = 20M

1. Explain secondary data

2. What are the applications of statistics to various disciplines

3. What are the rules of tabulation

4. Describe Pie charts

5. Define coefficient of variation

6. Write the uses of geometric mean

7. Define Lorenz curve

8. Define frequency polygon

SECTION-BAnswer ALL the questions. All questions carry equal marks. 4 x8 = 32M

9a) Explain various methods of collecting primary data.

b) Distinguish between a questionnaire and a schedule.How do you prepare a questionnaire and a schedule.

10a) Define classification of data and explain various ways of classification.

b) Discuss the importance of classification in statistics

11a) Explain the rules for construction of Bar diagrams and Histogram.

b) Explain the usefulness of diagrams. Construct Histogram and frequency polygon for the following data

Class Interval

0-10 10-20 20-30 30-50 50-60 60-70

Frequency 12 15 20 10 14 9

12a) Explain any two measures of central tendency

b) Explain various measures of dispersion.

SECTION-CAnswer ALLthe questions. All questions carry equal marks. 8x1=8M

13) What is statistical enquiry

14) Define complex table

15) Define ogives

16) Give the formula for median

17) Define coefficient of variation

18) What are deciles and percentiles

19) Define Harmonic mean

20) Find A.M of the numbers 2, 5, 5, 6, 7.

GOVERNMENT COLLEGE (A) , RAJAHMUNDRYIIB.A. SEMESTER:III

(For Non-Mathematics Combination)Module 3 : Statistical Methods-I

(Without mathematical derivations)Total hrs per week ;04 Total no. of credits: 03-------------------------------------------------------------------------------------------Unit- I

Attributes- Classes, 2x2, manifold classification, class frequencies, ultimate class frequencies, Contingency tables, association and independence of attributes, consistency of data, coefficient of colligation.

Unit-IIMoments: Central and non-central moments, Sheppard’s corrections for moments Skewness , kurtosis and their measures.

Unit-IIIProbability: Definitions of random experiment, outcome, sample space, event, mutually exclusive event, equally likely events, favourable events, classical, statistical and axiomatic definitions of probability. Addition and multiplication theorems for two events, Conditional probability. Baye’s theorem statement and problem based on ot.

Unit- IVRandom Variable: Discrete-Probability mass function, Continuous random variable-Probability density function, distribution function of a random variable and properties.

Unit-VMathematical Expectation: Basic results & properties of M.G.F, C.G.F, P.G.F and C.F

Text Books:1. S.P.Gupta: Statistical Methods . Sultan Chand2. Sambavyata - Telugu Academy3. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics.

Reference Books:1. .Goon, Gupta and Das Gupta: Fundamentals of Statistics . Volume I .World Press.2. . K.V.S. Sarma: statistics Made Simple: do it yourself on PC. PHI

Practicals-Semester-III1. Non central moments2. Central moments3. Sheppard’s corrections4. Skewness and kurtosis5. Coefficients of association and colligation6. Baye’s theorem-problems.

GOVERNMENT COLLEGE (A) , RAJAHMUNDRYIIB.A. SEMESTER:III

(For Non-Mathematics Combination)Module 3 : Statistical Methods-I

(Without mathematical derivations)Time; 3hrs MODEL PAPER Max Marks: 75

SECTION-AAnswer All the questions: All questions carry equal marks. 4 x10=40M

1a) Write the consistency conditions for a given data for (i) single attribute (ii) two attributes and (iii) three attributes.

(OR)b) Using the following given class frequencies, find the remaining class

frequencies.

N = 23,713, (A) =1618, (B) = 2015, (C) = 770, (AB) = 587, (AC) = 428,

(BC) = 335, (ABC) = 156

2a) Define (i) Raw moments (ii) Central moments. Express the central moments interms of raw moments.

(OR)

b) Explain various measures of skewness.

3a) Define (i) Classical definition of probability(ii) Statistical definition of probability(iii) Axiomatic definition of probability

and write their limitations.

(OR)

b) State and prove Addition theorem of probability for two events.

4a) A random variable X has the following probability function

X = x 0 1 2 3 4 5 6 7P(X=x) 0 k 2k 2k 3k K2 2k2 7k2+k

Find K, P ( X < 6 ), P ( X ≥ 6) , P ( 0 < X < 5)

(OR)b) Prove the following results

(i) E ( X + Y ) = E (X) + E (Y)(ii) E (XY) + E(X) E(Y)

SECTION-BAnswer any FIVE of the following questions. 5 x 3 = 15M

5 Explain independence of two attributes

6 Explain Yule coefficient of association

7 Explain about kurtosis

8 Define (i) Mutually exclusive events(ii) Exhaustive events(iii) Equally likely events

9 A 100 page book is opened at random. What is the probability that the page opened is having a prime number.

10 Write the properties of Distribution function.

11 If X is a random variable, then show that V(ax + b) = a2 v(X), where a and b are Constants

12 Define M.G.F and write its properties

SECTION-CAnswer All the questions: All questions carry equal marks. 10x2=20M

13. Define an attribute14. Define Yule’s coefficient of colligation

15. Give the sheppard’s corrections for moments

16. What are the limits of Skewness

17. Define sample space

18. Define conditional probability

19. Define Discrete random variable

20. Define probability mass function

21 Define Cumulant generating function (C.G.F)

22 . Define characteristic function.

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GOVERNMENT COLLEGE (A) , RAJAHMUNDRYIIB.A. IV SEMESTER:

(For Non-Mathematics Combination)Module 4: Statistical Methods-II

(Without mathematical derivations)Total hrs per week:04 Total no. of credits: 03-------------------------------------------------------------------------------------------Unit-IDiscrete distributions: Binomial, Poisson, Geometric distributions-

definitions,means, variances and applications of these distributions. Additive property if exists. Simple problems.

Unit- IIContinuous distributions: Rectangular, Normal, exponential distributions-definitions and their properties.Simple problems.

Unit-IIICurve fitting: principle of least squares-fitting of straight line, Parabola, exponential and power curves.

Unit-IV:Correlation and Regression:Meaning, types, scatter diagrams, correlation-coefficient, Spearman’s rank correlation, Regression lines, Regression coefficients and their properties.

Unit-V

Interpolation: Need and meaning of Interpolation, Graphical method. Newton’s and Lagrange’s formula for Interpolation

Text Books:1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics.

2. Statistical methods- S.P.Gupta..Reference Books:

1. Saha Sambandham Vibhajana Siddhantamu Vol.- I & Vol. – II .Telugu Academy

2. Sambavyata - Telugu Academy3. Sankyka Vislashanamu – Telugu Academy

4. .Goon, Gupta and Das Gupta: Fundamentals of Statistics . Volume I .World Press.

Practicals- Semester-IVConduct any 6 practicals

1. Fitting of Binomial by direct method2. Fitting of Poisson distribution by Direct method3. Fitting of Normal distribution by Ordinates method4. Fitting of Straight line5. Fitting of Parabola6. Fitting of Y = a Xb

7. Fitting of Y = a bx

8. Fitting of Y = a ebx

9. Correlation coefficient for ungrouped data10. Regression lines.

GOVERNMENT COLLEGE (A) , RAJAHMUNDRYIIB.A. SEMESTER:IV

(For Non-Mathematics Combination)Module 4 : Statistical Methods-II



1a) Define Binomial distribution and discuss its properties.

(OR)b) Define Geometric distribution. Obtain its mean and variance.

2a) Define Normal distribution. Explain its frequency curve? Mention its properties.

(OR)b) Define and Explain Exponential distribution. Discuss about its importance

3a) How do you fit a curve y = a ebx to the given data using the method of least squares

(OR)b) Fit a straight line Y = a + bx to the following data by the method of least squares.

X 4 6 8 10 12y 14 15 17 20 22

4a) In the following data, we are given the sales of a businessof a company in thousands of rupees. Using Newton’s interpolation formula find out the sales in the year 1997.

.Year 1996 1998 2000 2001 2004

Sales(in thou 40 19 48 50 57

b) Following are the marks of 10 students in two subjects Mathematics and Statistics. Calculate rank correlation coefficient.

Student 1 2 3 4 5 6 7 8 9 10

MarksinMath 75 90 80 59 54 64 87 93 84 97

Marks in Stat 60 50 78 58 45 42 75 82 95 88


5 Define poisson distribution and obtain its mean and variance

6 Explain Rectangular distribution and state its properties

7 Explain principle of least squares

8 Explain Scatter diagram

9 Write the properties of regression coefficients

10 Explain the need of interpolation

11 Explain Graphical Method

12 Explain the importance of normal distribution.

SECTION-CAnswer All the questions: All questions carry equal marks. 10x2=20M13. State additive property of poisson distribution

14. Write applications of Binomial distribution

15. Write the mean and variance of Rectangular distribution

16. Write P.d.f of normal distribution

17. Write the normal equations of a straight line.

18. Define Correlation and Regression

19. What is the product of two regression coefficients

20. Define Lagrange’s formuls of interpolation

21 Write the regression line of Y on X

22 . What are the limits of spearman’s rank correlation

Government College (A) RajahmundryB.A/B.Sc. III Year: Statistics Syllabus(For Non-Mathematics Combination)

Semester-V CBCSModule 5 : Statistical Applications-I

(Without mathematical derivations)Total hrs per week: 03 Total credits:03

Unit-IStatistical Inference:-Estimation:Definitions of population, sample, parameter, statistic, sampling distribution of a statistic, standard error. Estimation-Criteria of a good estimator, meaning of interval estimation

Unit-IIStatistical Hypothesis-Large sample test: Null and alternative hypothesis, level of significance, Type I and Type II errors, power of the test. Large sample tests for proportion (single & double), means(single & double), and standard deviations.

Unit-IIISmall sample tests: Tests of significance based on chisquare, t and F, chisquare test for independence of attributes, t-test for single, double and paired tests,Variance Ratio test (F-test)Unit-IVNon-Parametric tests: Advantages, Disadvantages, sign test, median test and run test for two sample cases only.

Unit-VIndex numbers: Definition and meaning of Index Numbers. problems involved in the construction of index numbers , Simple and Weighted Index Numbers-Laspeyre’s Paasche’s and Fisher’s indices. Cost of living index numbers.Text Books: 1. Statistical methods-S.P.Gupta

2 Fundamentals of statistics-Goon Gupta and Das Gupta Vol I and Vol IIReference Books:

1.Anuvarthitha Sankyaka Sastramu – Telugu Academy book.

2.Applied Statistics-V.K.Kapoor & S.C.Gupta3.Applied Statistics-Parimal Mukhopadhyay.

Practicals-Semester-VConduct any 6 Practicals

1. Large sample tests-Mean(s)2. Large sample tests-Proportion(s)3. Small sample tests-t for Mean(s)4. F-test for variance ratio5. Chi square test for independence of attributes6. N.P.tests-Run test, Median test, Sign test.7. Laspeyre, Paasche, Fisher indices.

GOVERNMENT COLLEGE (A) , RAJAHMUNDRY IIIB.A. SEMESTER:V

(For Non-Mathematics Combination)Module 5 : Statistical Applications-I



1a) Explain the criteria of a good estimator

(OR)b) Define Statistic & Sampling distribution. Obtain the sampling distribution of mean X

2a) Explain the large sample test for testing the equality of two means.

(OR)b) In a survey of 900 people in Maharashtra, 540 are rice eaters and the rest are wheat

eaters. Can we assume that both rice and wheat are equally popular in the state at 1% level of significance.

3a) Explain chisquare test for independence ofattributes.

(OR)

b) The following data are two samples of sizes 10, 12 drawn from two normal populations. Test the significant difference between variances of two samples.

First Sample 10, 6, 16, 17, 13, 12, 8 15, 9, 14Second Sample 7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 7

4a) Explain the run test for testing the equality of two distribution functions

(OR)

b) Discuss the advantages and disadvantages of Non parametric methods. Explain sign test for one sample.

5a) Define an Index Number. Distinguish between simple and weighted index numbers.

b) Explain the problems involved in the construction of index numbers


5 Explain standard error

6 Explain interval estimation

7 Explain Type I and Type II errors

8 Explain test for standard deviations

9 Explain paired t test

10 Explain cost of living indx numbers

11 Explain Fisher’s ideal index number

12 Distinguish between large sample tests and small sample tests


13. Define population

14. Define random sample

15. Define Null hypothesis

16. Define level of significance

17. Write properties of F-distribution

18. Define t-test for single mean

19. Define Non-parametric test

20. What is the purpose of an index number

21 Define cost of living index numbers

22 . Define Laspeyre’s index number

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(Examination at the end of V semester)Module 6 : Sampling Techniques (Elective-I)

(Without Mathematical derivations)Total hrs per week:03 Total credits: 03---------------------------------------------------------------------------------Unit-ISampling theory: Population, sample, sampling versus census, sample survey meaning, Sampling and Non-sampling errors, Limitations of sampling

Unit-IISampling Methods: Principle steps in a sample survey. Types of sampling- Simple random sampling, Stratified random sampling, Systematic sampling.

Unit-IIISimple Random Sampling method: SRSWR, SRSWOR, Random number table method and lottery system method. Sample mean is an unbiased estimate of population mean, sample mean of variance.

Unit-IVStratified Random Sampling: Meaning of stratified random sampling, merits and demerits. Definitions of Proportional and Optimum allocations.

Unit-V:Systematic Random Sampling: Definition of systematic random sampling. Comparison of SRSWOR (problem), stratified and systematic samplings.

Text Books: 1. Statistical methods-S.P.Gupta2 Fundamentals of statistics-Goon Gupta and Das Gupta Vol I and Vol II

Reference Books:1.Anuvarthitha Sankyaka Sastramu – Telugu Academy book.


Practicals-Semester-V1. Estimation of Population mean in SRSWR2. Estimation of population variance in SRSWR3. Estimation of population mean in SRSWOR4. Estimation of population variance in SRSWOR5. Comparison of SRSWOR with optimum and proportional allocations6. Comparison of SRSWOR, stratified and systematic samplings.


(For Non-Mathematics Combination)Module 6: Sampling Techniques (Elective-I)



1a) Discuss advantages of sampling over complete census, Under what circumstances can complete enumeration be recommended in preference to a sample survey.

(OR)b) Discuss sampling and non sampling errors

2a) What are the main steps involved in a sample survey? Discuss them.

(OR)

b) Explain about different types of sampling

3a) Explain the methods of drawing simple random sampling with replacement

(OR)b) Define Simple random sampling. Show that sample mean is an unbiased estimator of

population mean in SRSWOR

4a) Describe the procedure of stratified random sampling. Under what conditions is stratified random sampling preferred to simple random sampling and why?

(OR)b) Explain proportional and optimum allocations in stratified random sampling

5a) Explain systematic sampling with suitable example

(OR)b) How do you compare systematic sampling with SRSWOR


5 Explain types of collecting information

6 Explain the limitations of sampling

7 Explain Mixed sampling

8 Explain SRSWR and SRSWOR

9 What are merits and demerits of stratified random sampling

10 Explain stratification

11 Explain systematic sampling

12 Distinguish between stratified and systematic samplings.


13. Define population

14. Define random sample

15. What are the main objectives of a survey

16. Define simple random sampling

17. Define stratum

18. Define allocation of sample size

19. What is the variance of SRSWOR

20. Define sampling frame

21 write the merits of systematic sampling

22 . Whar are types of sampling

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(Examination at the end of VI semester)Module 8: Statistical Applications-II

(Without mathematical derivations)Total hrs per week:03 Total credits:03--------------------------------------------------------------------------------------------

Unit-IVital Statistics: Meaning, definition, uses, source of vital statistics – registration method, census method Death rates-, crude death rates – age specific death rate, standardized death rates Birth rates- – crude birth rate, age specific fertility rate, general fertility rate, total fertility rate.Unit_IIReproductive rates: Gross reproductive rate and net reproductive rate – life tables and abridged life tables.

Unit-IIITime series: Meaning components, trend- graphical, semi-averages, straight line, parabola, moving average methods. Seasonal indices methods- simple averages –ration to trend, ratio to moving average , link relatives methods.Unit-IV(SQC): Importance of SQC in industry – Concept of chance and assignable causes of variation, Natural tolerance and pecification limits,

Unit-V

Control Charts for variables (Mean, Range, charts) and attribute (p, np and C) Charts for fixed sample size only.Text Books: 1. Statistical methods-S.P.Gupta

2 Fundamentals of statistics-Goon Gupta and Das Gupta Vol I and Vol IIReference Books:

4.Anuvarthitha Sankyaka Sastramu – Telugu Academy book.


Practicals-Semester-VConduct any 6 Practicals

1. Birth rates2. Death rates3. Trend-Straight line4. Seasonal indices-Simple Average5. X, R charts6. Attribute control chart p chart7. Attribute control chart np chart


(For Non-Mathematics Combination)Module 8: Statistical Applications-II



1a) Explain Vital statistics. What are the sources of vital statistics? Explain

(OR)b) What are mortality rates? Explain them

2a) Explain Reproductive rates

(OR)b) Explain the construction of life tables

3a) Explain the various components of time series.

b) Explain the method of moving average in measuring trend

4a) Explain the importance of SQC in industry

(OR)b) Explain the following:

(i) Chance causes(ii) assignable causes(iii) Natural tolerance limits

5a) Explain the construction of X , R charts

(OR)b) Distinguish between variable control charts and attribute control charts.


5 Explain total fertility rate and age specific fertility rate

6 Explain abridged life tables

7 Explain the determination of trend by semi averages method

8 Explain link relatives method

9 Write the uses of SQC

10 Explain specification limits

11 Explain C Chart

12 Describe a life table


13. Define Vital statistics

14. Define Gross reproduction rate

15. Write about the force of mortality

16. Define crude death rate

17. Define trend

18. Write the normal equations in fitting a straight line

19. Give an example for irregular variations

20. Define defective item

21 Define time series

22 . What is SQC?

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(Examination at the end of VIsemester)Elective-II

Module 97: Testing of HypothesisWithout mathematical derivations

Unit-ITests of significance – concepts of null and alternative hypothesis, level of significance, type-I and type-II errors – power of the test –Critical region, Neyman Pearson’s Lemma.

Unit-IILarge sample tests for proportion(s), mean(s) and Standard deviations

Unit-IIISmall sample tests – Using t, F and Chi-square tests. X2 test for goodness of fit and test for independence of attribues.

Unit-IV

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

Recommended Books:List of Reference Books:1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand&Sons, New Delhi2. Goon AM, Gupta MK,Das Gupta B : Outlines of Statistics , Vol-II, the World Press Pvt.Ltd., Kolakota.3. Hoel P.G: Introduction to matehematical statistics, Asia Publiushing house.4.Sanjay Arora and Bansi Lal:.New Mathematical Statistics Satya Prakashan , New Delhi5.Hogg and Craig :Introduction to Mathematical statistics. Printis Hall6.Siegal,S.,and Sidney: Non-param etric statistics for Behavioral Science. McGraw Hill.7GibbonsJ.D and Subhabrata Chakraborti: Nonparametric Statistical Inference. Marcel Dekker.8.Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.


(Examination at the end of VI semester)Elective-II

Module 9 : Design of Experiments and Official statisticsTotal hrs per week:03 Total credits:03-------------------------------------------------------------------------------Unit-IOfficial Statistics: National income, methods to estimate national income, problems involved in estimating national income, agricultural statistics.

Unit-IIArea, yield of statistics, Functions and organization of CSO, NSSO

Unit-IIIAnalysis of variance: Meaning, definition, assumptions, one way and two way classifications.

Unit-IVPrinciples of design of experiments: Principles of experiment, Completely Randomized design, Randomized block design and Latin square design.

Unit-VMissing plot techniques: RBD, LSD, Concepts of Factorial experiments 22 , 23

Text Books:1. Fundamentals of Statistics: Goon Gupta, Das Gupta2. Applied Statistics-Parimal Mukhopadhyaya

Reference Books1. Design of Experiments by Gupta Kapoor:2. Applied Statistics-V.K.Kapoor & S.C.Gupta3. Anuvarthitha Sankyaka Sastramu – Telugu Academy book.

Practicals-Semester-VI1. ANOVA-equal one way classifications2. ANOVA-unequal one way classifications3. ANOVA-Two way classifications4. CRD5. RBD6. LSD


(For Non-Mathematics Combination)Module 8: Statistical Applications-II



1a) Discuss the problems involved in measuring national income.జా?య దయ మదింపుల? ఎ ర ే? సమస?లనూ చ ?ంచ మ .

(OR)b) Discuss the various methods to estimate the National income

జా?యదయ ? ? అంచన వ ప ?త లన ? ంపుమ .

2a) Explain the functions of C.S.OC.S.O ? క? ?ధ ల ఏ? ?

(OR)b) Explain the functions of N.S.S.O

N.S.S.O ? క? ?ధ ల ఏ? ?

3a) Explain ANOVA one way classificationఎక?ధ ?స?ృ? ? ?షనన ? ంపుమ .

(OR)b) Define and Explain ANOVA? Write its assumptions

?స?ృ? ? ?? ? ? ? ర?? ం? ? ంపుమ మ య ద ? ? క? ఉపకల?నలన వ?య మ .

4a) Explain the basic principles of experimental design.ప?? గ రచనల ? క? ? ? క సూ ?లన ? ంపుమ .

(OR)b) Explain the layout and analysis of R.B.D

య ృ? ?క కండ రచన ? క? ర పణ మ య ? ??షణన ? ంపుమ .

5a) Explain the missing plot technique of L.S.Dల? ం?న ఖం ?క ప ?? అన ? .

(OR)b) Explain 22 factorial experiment.

22రక ప?? గపు ? ??షణన ? ంపుమ .

Answer any FIVE of the following questions. 5 x 3 = 15M

6 Explain national incomeజ ?య య ?? ?వ ంప మ .

7 Explain agricultural statistics? య గణ ం ల?? ? ంపుమ .

8 Expla

9 Write the uses of SQCంఖ?క ణ ?యం ?ణ ఉప? గ ల ?య మ .

10 Explain specification limitsస? ?ీకరణ అ ధ ల ? ంపుమ ?

11 Explain C ChartC ా?? ?వ ంప మ .

12 Describe a life table

? న పట?క ? ంపుమ .

G-overnment College (A) RajahmundryB.A/B.Sc. III Year: Statistics Syllabus(For Non-Mathematics Combination)

(Examination at the end of VI semester)Elective-II

Module 10 : Operations Research

Unit-1Definition and scope of operations research, Phases in operations research, and theirSolutions, Linear programming, Formulation of LPP, Solving the LPP by graphical Method.

Unit-II

Transportation Problem:Definition of transportation problem, TPP as a special case of LPP, feasible solutions by North-West and Matrix minimum methods and VAM.

Unit-IIIGame theory: Two person games, pure and mixed strategies , zero sum games finding solutions in 2x2 and 2xm games

Unit - IVAssignment problem: Formulation and description of Assignment problem and its variations. Assignment problem as special case of TP and LPP. Unbalanced assignment problem, traveling salesman problem. Optimal solution using Hungarian method.

Recommended Books:

1. Kanti Swaroop,P.K.Gupta and ManMohan: Operations Research. Sultan Chand.2. Gass: Linear Programming. Mc Graw Hill.3. Hadly : Linrar programming. Addison-Wesley.4.Wayne L. Winston : Operations Research. Thomson, India edition. 4th edition.5. Taha : Operations Research: An Introduction : Mac Millan.

BASIC CURRICULAR FORMAT UNDER MODULAR AND CBCS SYSTEM

Subject : B.A Statistics (First Year) Semester : 1

Name of the Module : Elementary Mathematics & Descriptive SstatisticsNature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60

Sl.No. Mon & Week No. of hrs

Topic Curricularactivity

Co-curricular activity

Remarks

01 June III 04 Concept of sequences and series, fundamentals of sets and functions, types of functions

02 June IV 04 Solution of simultaneous linear equations

Problem solving

Assignment

03 July I 04 Quadratic equations finding roots

Problem solving

Assignment

04 July II 04 Progressions AP,GP,HP

Problem solving

July 11 th World population day celebration

05 July III 04 Permutations and combinations,Binomial theorem

Problem solving

Assignment

06 July IV 04 Matrices addition subtraction, multiplication of matrices

Problem solving

I internal exam

O7 August I 04 Determinant, transpose, inverse and rank of matrix

Problem solving

08 August II 04 Solution of simultaneous linear equations by matrix methods, Cramer’s rule

Problem solving

09 August III 04 Matrix inversion method

Problem solving

10 August IV 04 Measures of central tendency,AM,GMand HM

Problem solving

11 Sept ember I 04 Median II internal exams

12 September II 04 Modeand quantiles

Problem solving

13 September III 04 Primary and secondary data methods of collection of primary data

14 September IV 04 Sources of secondary dataclassification and tabulation

15 October I 04 Revision of the syllabus

16 October II 04 Solving the old

question papers17 October III 04 Semester

end examinations

18 October IV 04 ,,


Subject : B.Sc Statistics (First Year) Semester : 1I

Name of the Module : Elementary Mathematics and Descriptive statisticsNature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 November I 04 Data presentation Bar diagrams, two dimensional diagrams and pie chart

02 November II 04 Graphs-Histogram, frequency polygon, frequency curve and ogive

Drawing charts

Assignment

03 November III 04 Measures of dispersion, range, Quartile deviation

Problem solving

Assignment

04 November IV 04 Standard deviation andMean deviation

Problem solving

Assignment

05 December I 04 Measures of relative variation coefficient of variation

Problem solving

06 December II 04 Revision Problem solving

I internal exam

O7 December III 04 Differentiation, differential coefficient of algebraic and exponential functions

Seminar by students

08 December IV 04 Maxima and Minima of a function

Seminar by students

09 January I 04 Partial derivatives

10 January II 04 Integration Assignment

11 January III 04 Integration by parts

II internal exams

12 January IV 04 Integration by substitution

13 February I 04 Practicalscorrection

14 February II 04 Practicals15 February III 04 Practicals16 February IV 04 Practicals17 March I 04 Revision of the

syllabus18 March II 04 Solving the old

question papers,,

19 March III 04 Semester end examinations


Subject : B.A Statistics (Second Year) Semester : I1I

Name of the Module : Statistical Methods-INature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 June III 04 Attributes classification of data double and manifold class frequencies and ultimate class frequencies.

02 June IV 04 Concept of Association and Independence

Problem solving

Assignment

03 July I 04 Consistency of data measures of association and

Problem solving

Assignment

Yule’s coefficient of colligation

04 July II 04 Central and noncentral moments and their interrelationships, sheppard’s corrections

Problem solving


05 July III 04 Measures of skewness based on quartiles and moments

Problem solving

Assignment

06 July IV 04 Kurtosis based on moments

Problem solving

I internal exam

O7 August I 04 Probabilty definitions

Problem solving

08 August II 04 Addition and multiplication heorems

Problem solving

09 August III 04 Conditional probability Statement of Baye’s theorem and simple examples

Problem solving

10 August IV 04 Random variable, discrete and continuous rv’s,p.m.f and p.d.f

Problem solving

Assignment

11 Sept ember I 04 Distribution functionfor both discrete and continuous r.v

II internal exams

12 September II 04 Mathematical expectation,definition statement of its basic results and some simple problems

Problem solving

13 September III 04 Revision for slow learners

14 September IV 04 revision15 October I 04 Revision of the

syllabus

16 October II 04 Solving the old question papers

17 October III 04 Semester end examinations

18 October IV 04 ,,


Subject : B.Sc Statistics (Second Year) Semester: 1V

Name of the Module : Statistical Methods-IINature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 November I 04 Definition, properties and applications of Bernoulli, Binomial, Poisson distributions

Problem solving

02 November II 04 Negative Binomial, geometric, Hypergeometric distributions

Problem solving

Assignment

03 November III 04 Normal, Exponential distributions

Problem solving

Assignment

04 November IV 04 Interpolation, Methods of interpolation, Graphic method

Problem solving

Assignment

05 December I 04 Finite difference, Binomial expression method

Problem solving

06 December II 04 Newton’s and Lagrange’s formula for interpolation

Problem solving

I internal exam

O7 December III 04 Curve fitting principle of least squares, fitting of straight line, and parabola

Seminar by students

08 December IV 04 Fitting of exponential and logarithm curves

Seminar by students

09 January I 04 Correlation, types of correlation, scatter diagram correlation coefficient

10 January II 04 Spearman’s rank correlation coefficient with repeated ranks

Problem solving

Assignment

11 January III 04 Regression, Lines of regression

Problem solving

II internal exams

12 January IV 04 Regression coefficients and their properties

13 February I 04 revision14 February II 04 Practicals15 February III 04 practicals16 February IV 04 practicals17 March I 04 Revision of the

syllabus18 March II 04 Solving the old

question papers,,

19 March III 04 Semester end

examinations


Subject : B.Sc Statistics (Third Year) Semester : V

Name of the Module : Statistical Quality Control (P-IV)Nature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 June II 07 Admission work and Introduction on SQC

02 June III 07 Control Charts for Variables, X, R, σ charts, their construction and interpretation

Practical-1, 2

03 June IV 10 Control charts for Attributes, P, np and C Charts, their construction and interpretation

Practical-3, 4

04 July I 0905 July II 04

06 July III Pushkara Holidays 14th to 25th

07 July IV 08O8 August I 1009 August II 0710 August III 05 First

Internal Exams

11 August IV 1112 Sept ember I 0413 September II 0414 September III 0415 September IV 0416 October I 04 Revision of the

syllabusSecond Internal Exams

17 October II 04 Solving the old question papers

18 October III Dasara Holidays

19 October IV ,,Semester end examinations

20 November I ,,,,,,,,


Subject : B.A Statistics (Third Year) Semester : V

Name of the Module : Sampling Techniques and Design of ExperimentsNature of the module : Core

Nature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 November I 04 Sampling versus census, planning organization and execution of sample surveys

Problem solving

02 November II 04 Sampling and nonsampling errors, limitations of sampling

03 November III 04 Probability and non probability sampling schemes

04 November IV 04 Random number tables and drawing of random samples

05 December I 04 Simple random sampling

Problem solving

06 December II 04 Stratified random sampling

Problem solving

I internal exam

O7 December III 04 Allocation of sample size under proportional and optimum allocation

Seminar by students

08 December IV 04 Systematic sampling-linear and circular

Seminar by students

09 January I 04 Revision on Unit-I

10 January II ……

11January III 04 Unit test-1 II internal

exam12 January IV 04 revision13 February I 04 Project

work14 February II 04 Practicals15 March I 04 Revision

16 March II 04 Revision17 March III 04 Revision 18 March IV 04 Semester

end xams


Subject : B.A Statistics (Third Year) Semester : VI

Name of the Module : Statistical Applications-IINature of the module : Core

Nature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 June III 04 Vital statistics, registration method, census method

02 June IV 04 Mortality rates Problem solving

Assignment

03 July I 04 Fertility rates Problem solving

Assignment

04 July II 04 Time series-components determination of trendby graphical and semi averages method

Problem solving


05 July III 04 Least squares and moving average methods

Problem solving

Assignment

06 July IV 04 Seasonal indicesby simple average

Problem solving

I internal exam

O7 August I 04 Ratio to trend method

Problem solving

08 August II 04 Ratio tomoving average method

Problem solving

09 August III 04 Link relatives method

10 August IV 04 Statistical process control, chance and assignable causesof variation

Problem solving

Assignment

11 Sept ember I 04 Control charts for variables

II internal exams

12 September II 04 Control charts for variables

Problem solving

13 September III 04 Control charts for attributes

14 September IV 04 Process capability index and its uses

15 October I 04 Revision16 October II 04 Solving the old

question papers17 October III 04 Semester

end examinations

18 October IV 04 ,,


Subject : B.A Statistics (Third Year) Semester :VI

Name of the Module : Sampling Techniques and Design of Experiments-IINature of the module : CoreNature of learning : RegularNo. of hours/week : 04 Credits : 03 Total Hours : 60




Remarks

01 November I 04 Sampling versus census, planning organization and execution of sample surveys

Problem solving

02 November II 04 Sampling and nonsampling errors, limitations of sampling

03 November III 04 Cluster sampling two stage with equal no of clusters

04 November IV 04 National income,method of estimating national income

05 December I 04 Functions and organization of CSO and NSSO

Problem solving

06 December II 04 Analysis of variance-one way classification

Problem solving

I internal exam

O7 December III 04 ANOVA-two way classification

Seminar by students

08 December IV 04 Principles of design of experiments

Seminar by students

09 January I 04 CRD10 January II RBD

January III 04 LSD II internal

11 exam12 January IV 04 22 experiment13 February I 04 23 experiment Project

work14 February II 04 Practicals15 March I 04 Revision16 March II 04 Revision17 March III 04 Revision 18 March IV 04 Semester

end xams

GOVERNMENT COLLEGE (A) : RAJAHMUNDRY B.A I Year ...gcrjy.ac.in/departments/syllabus/d9fc5b73a8d78fad3d6dffe419384e… · Practicals- Semester-I Conduct any 6 Practicals. 1. Solution

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