GOVERNMENT COLLEGE (A) : RAJAHMUNDRY B.A I Year...

GOVERNMENT COLLEGE (A) : RAJAHMUNDRY

B.A I Year: Statistics Syllabus

(For Non-Mathematics Combination)

Semester-I CBCS Module 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 Matrix

Inversion methods.

Unit-V

Differentiations: 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 Chand

2)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 equations

2. Progressions- AP, GP, HP

3. Addition, Subtraction, Multiplication of Matrices.

4. Determinant of a Matrix

5. Solution of equations by Matrix methods.

6. Simple differentiation

7. Integrations

GOVERNMENT COLLEGE (AUTONOMOUS)

RAJAMAHENDRAVARAM

FIRST SEMESTER END EXAMINATION

I BA – STATISTICS (SEMESTER-I)

ELEMENTARY MATHEMATICS Time: 3hrs Max Marks-60

MODEL PAPER

SECTION –A

5x4=20M

Answer any five of the following.

1. Obtain the roots of the quadratic equation ax2 + bx +c =0

ax2 + bx +c =0 అఅఅ అఅఅఅ అఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅ

అఅఅఅఅఅఅఅఅ.

2. Explain permutation and combination with examples.

అఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅ అఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ.

3. Write short notes on Arithmetic progression

అఅఅఅఅఅ అఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅ.

4. Define finite set. అఅఅఅఅఅ అఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅఅ

5. nc3 =nc5 find n .

nc3 =nc5 అఅఅఅఅ n అఅఅఅఅ అఅఅ?

6. Define matrix and its properties అఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ అఅఅఅ అఅఅఅఅ అఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅఅ.

7. State and explain Binomial theorem

అఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ.

8. Find the derivative of Y = X2 + 2X + 1 Y = X2 + 2X + 1 అఅఅఅఅ అఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅ.

SECTION-B

Answer all the questions: 4x8=32M

9a) If A= B= and C=

Prove the following equation

A= B= and C= అఅఅఅఅఅఅఅఅఅ

అఅ అఅఅఅఅఅఅఅఅఅఅ.

(OR)

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

x2+4x +3 = 0 అఅఅ అఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ అఅఅఅఅ అఅఅఅఅఅఅఅఅఅ

అఅఅఅఅఅఅఅఅ.

10a)

Find sum of ‘n’ terms of the series 7+77+777+……….

7+77+777+………. అఅఅ అఅఅఅఅఅ n అఅఅఅ అఅఅఅఅ అఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅ.

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)9 అఅ అఅఅఅఅఅఅఅఅ 6 అ అఅఅఅఅఅ అఅఅఅఅఅఅఅఅ.

(3x/7 – 2y)10 అఅఅఅఅఅఅఅఅ అఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅఅఅఅ.

11a)

Solve the following equations by cramer method

అఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅఅఅఅ.

(OR)

b) Solve the following equation s by inverse matrix method

అఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅ అఅఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅ అఅఅఅఅఅఅఅఅ

12a)

If A = then find A-1

(OR)

b) Evaluate

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GOVERNMENT COLLEGE (A) : RAJAHMUNDRY

B.A I Year: Statistics Syllabus


Semester-II CBCS Module-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.Gupta

2. Fundamentals of Mathematical Statistics- SC Gupta and V.K.Kapoor

3. 3.Moulika Ganithamu Sambavyata - Telugu Academy.

Reference Books:

4. Quantitative Techniques I-Sultan Chand Publication

Practicals- Semester-II

Conduct any 6 Practicals.

1. Arithmetic Mean, Median, Mode, GM, HM.

2. Calculation of CV and its comparisons.

3. Bar diagrams

4. Pie diagrams

5. Histogram

6. Frequency and Polygon.

7. 7.Ogive curves.

GOVERNMENT COLLEGE (AUTONOMOUS)

RAJAMAHENDRAVARAM

FIRST SEMESTER END EXAMINATION

I BA – STATISTICS (SEMESTER-II)

DESCRIPTIVE STATISTICS Time: 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-B

Answer 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-C

Answer 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) , RAJAHMUNDRY

IIB.A. SEMESTER:III


Module 3 : Statistical Methods-I

(Without mathematical derivations)

Total hrs per week ;04 Total no. of credits: 03

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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-II

Moments: Central and non-central moments, Sheppard’s corrections for

moments Skewness , kurtosis and their measures.

Unit-III

Probability: 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- IV

Random Variable: Discrete-Probability mass function, Continuous random

variable-Probability density function, distribution function of a random variable

and properties.

Unit-V

Mathematical 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 Chand

2. Sambavyata - Telugu Academy 3. 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-III

1. Non central moments

2. Central moments

3. Sheppard’s corrections

4. Skewness and kurtosis

5. Coefficients of association and colligation

6. Baye’s theorem-problems.


IIB.A. SEMESTER:III


Module 3 : Statistical Methods-I


Time; 3hrs MODEL PAPER Max Marks: 75

SECTION-A

Answer 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 7

P(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-B

Answer 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-C

Answer All the questions: All questions carry equal marks. 10x2=20M

13. Define an attribute

14. 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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IIB.A. IV SEMESTER:


Module 4: Statistical Methods-II


Total hrs per week:04 Total no. of credits: 03

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Unit-I

Discrete distributions: Binomial, Poisson, Geometric distributions-

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

exists. Simple problems.

Unit- II

Continuous distributions: Rectangular, Normal, exponential distributions-

definitions and their properties.Simple problems.

Unit-III

Curve 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 Academy 3. Sankyka Vislashanamu – Telugu Academy

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

Practicals- Semester-IV

Conduct any 6 practicals

1. Fitting of Binomial by direct method

2. Fitting of Poisson distribution by Direct method

3. Fitting of Normal distribution by Ordinates method

4. Fitting of Straight line

5. Fitting of Parabola

6. Fitting of Y = a Xb

7. Fitting of Y = a bx

8. Fitting of Y = a ebx

9. Correlation coefficient for ungrouped data

10. Regression lines.


IIB.A. SEMESTER:IV


Module 4 : Statistical Methods-II


Time; 3hrs MODEL PAPER Max Marks: 75

SECTION-A


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 12

y 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

SECTION-B


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-C


13. 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) Rajahmundry

B.A/B.Sc. III Year: Statistics Syllabus


Semester-V CBCS

Module 5 : Statistical Applications-I (Without mathematical derivations)

Total hrs per week: 03 Total credits:03

Unit-I

Statistical 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-II

Statistical 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-III

Small 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-IV

Non-Parametric tests: Advantages, Disadvantages, sign test, median test and run test for

two sample cases only.

Unit-V

Index 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 II

Reference Books:

1. Anuvarthitha Sankyaka Sastramu – Telugu Academy book.

2. Applied Statistics-V.K.Kapoor & S.C.Gupta

3. Applied Statistics-Parimal Mukhopadhyay.

Practicals-Semester-V

Conduct 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 ratio

5. Chi square test for independence of attributes

6. N.P.tests-Run test, Median test, Sign test.

7. Laspeyre, Paasche, Fisher indices.


IIIB.A. SEMESTER:V


Module 5 : Statistical Applications-I

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

SECTION-A


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, 14

Second 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

SECTION-B


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

SECTION-C


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

------------------------




(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-I

Sampling theory: Population, sample, sampling versus census, sample survey meaning,

Sampling and Non-sampling errors, Limitations of sampling

Unit-II

Sampling Methods: Principle steps in a sample survey. Types of sampling- Simple

random sampling, Stratified random sampling, Systematic sampling.

Unit-III

Simple 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-IV

Stratified 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.



Reference Books:





1. Estimation of Population mean in SRSWR

2. Estimation of population variance in SRSWR

3. Estimation of population mean in SRSWOR

4. Estimation of population variance in SRSWOR

5. Comparison of SRSWOR with optimum and proportional allocations

6. Comparison of SRSWOR, stratified and systematic samplings.


IIIB.A. SEMESTER:V


Module 6: Sampling Techniques (Elective-I)


SECTION-A


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

SECTION-B


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.

SECTION-C


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

------------------------




(Examination at the end of VI semester)

Module 8: Statistical Applications-II (Without mathematical derivations)

Total hrs per week:03 Total credits:03

--------------------------------------------------------------------------------------------

Unit-I Vital 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_II

Reproductive rates: Gross reproductive rate and net reproductive rate – life tables and

abridged life tables.

Unit-III Time 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.



Reference Books:





Conduct any 6 Practicals

1. Birth rates

2. Death rates

3. Trend-Straight line

4. Seasonal indices-Simple Average

5. X, R charts

6. Attribute control chart p chart

7. Attribute control chart np chart


IIIB.A. SEMESTER:V


Module 8: Statistical Applications-II


SECTION-A


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.

SECTION-B


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

SECTION-C


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?

------------------------




(Examination at the end of VIsemester)

Elective-II

Module 97: Testing of Hypothesis Without mathematical derivations

Unit-I

Tests 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-II

Large sample tests for proportion(s), mean(s) and Standard deviations

Unit-III

Small 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 Delhi

2. 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

Delhi

5.Hogg and Craig :Introduction to Mathematical statistics. Printis Hall

6.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.





Elective-II

Module 9 : Design of Experiments and Official statistics

Total hrs per week:03 Total credits:03

------------------------------------------------------------------------------- Unit-I

Official Statistics: National income, methods to estimate national income, problems

involved in estimating national income, agricultural statistics.

Unit-II

Area, yield of statistics, Functions and organization of CSO, NSSO

Unit-III

Analysis of variance: Meaning, definition, assumptions, one way and two way

classifications.

Unit-IV

Principles of design of experiments: Principles of experiment, Completely Randomized

design, Randomized block design and Latin square design.

Unit-V

Missing plot techniques: RBD, LSD, Concepts of Factorial experiments 22 , 23

Text Books:

1. Fundamentals of Statistics: Goon Gupta, Das Gupta

2. Applied Statistics-Parimal Mukhopadhyaya

Reference Books

1. Design of Experiments by Gupta Kapoor:



Practicals-Semester-VI

1. ANOVA-equal one way classifications

2. ANOVA-unequal one way classifications

3. ANOVA-Two way classifications

4. CRD

5. RBD

6. LSD


IIIB.A. SEMESTER:V


Module 8: Statistical Applications-II


SECTION-A


1a) Discuss the problems involved in measuring national income.

జజజజజజజజజ జజజజజజజజ జజజజజజజజ జజజజజజజజ

జజజజజజజజజజ.

(OR)

b) Discuss the various methods to estimate the National income

జజజజజజజజజజజజజ జజజజ జజజజ జజజజజజజజజ

జజజజజజజజజజ. 2a) Explain the functions of C.S.O

C.S.O జజజజజ జజజజజజ జజజ? (OR)

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

N.S.S.O జజజజజ జజజజజజ జజజ? 3a) Explain ANOVA one way classification

జజజజజ జజజజజజజజ జజజజజజజజజజ జజజజజజజజజజ. (OR)

b) Define and Explain ANOVA? Write its assumptions

జజజజజజజజ జజజజజజజజజజజజ జజజజజజజజజజ

జజజజజజజజజజ జజజజజ జజజజ జజజజజ జజజజజజజజజజ

జజజజజజజజ. 4a) Explain the basic principles of experimental design.

జజజజజజ జజజజ జజజజజ జజజజజజజజ జజజజజజజజజ

జజజజజజజజజజ. (OR)

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

జజజజజజజజజ జజజ జజజ జజజజజ జజజజ జజజజజ

జజజజజజజజజజ జజజజజజజజజజ. 5a) Explain the missing plot technique of L.S.D

జజజజజజజజ జజజజజజజ జజజజజజ జజజజజజజజ. (OR)

b) Explain 22 factorial experiment.

22 జజజజ జజజజజజజజ జజజజజజజజజజ జజజజజజజజజజ.


6 Explain national income

అఅఅఅఅఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ.

7 Explain agricultural statistics

జజజజజజజ జజజజజజజజజజ జజజజజజజజజజ.

8 Expla

9 Write the uses of SQC

అఅఅఅఅఅఅ అఅఅ అఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅఅ అఅఅఅఅఅఅఅ.

10 Explain specification limits

జజజజజజజజజజ జజజజజజ జజజజజజజజజజ.

11 Explain C Chart

C అఅఅఅఅఅ అఅఅఅఅఅఅఅఅఅ.

12 Describe a life table

జజజజ జజజజజజ జజజజజజజజజజ.

G-overnment College (A) Rajahmundry




Elective-II

Module 10 : Operations Research

Unit-1 Definition and scope of operations research, Phases in operations research, and their

Solutions, 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-III

Game theory: Two person games, pure and mixed strategies , zero sum games

finding solutions in 2x2 and 2xm games

Unit - IV

Assignment 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 Sstatistics

Nature of the module : Core

Nature of learning : Regular

No. of hours/week : 04 Credits : 03 Total Hours : 60

Sl.No. Mon & Week No.

of hrs

Topic Curricul

ar

activity

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

Assignme

nt

03 July I 04 Quadratic

equations finding

roots

Problem

solving

Assignme

nt

04 July II 04 Progressions

AP,GP,HP

Problem

solving

July 11 th

World

populatio

n day

celebratio

n

05 July III 04 Permutations and

combinations,Bin

omial theorem

Problem

solving

Assignme

nt

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,GM

and 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 data

classification and

tabulation

15 October I 04 Revision of the

syllabus

16 October II 04 Solving the old

question papers

17 October III 04 Semester

end

examinati

ons

18 October IV 04 ,,


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

Name of the Module : Elementary Mathematics and Descriptive statistics





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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

Assignme

nt

03 November III 04 Measures of

dispersion, range,

Quartile deviation

Problem

solving

Assignme

nt

04 November IV 04 Standard

deviation and

Mean deviation

Problem

solving

Assignme

nt

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 Assignme

nt

11 January III 04 Integration by

parts

II internal

exams

12 January IV 04 Integration by

substitution

13 February I 04 Practicals

correction

14 February II 04 Practicals

15 February III 04 Practicals

16 February IV 04 Practicals

17 March I 04 Revision of the

syllabus

18 March II 04 Solving the old

question papers

,,

19 March III 04 Semester

end

examinati

ons


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

Name of the Module : Statistical Methods-I





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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

Assignme

nt

03 July I 04 Consistency of

data measures of

association and

Problem

solving

Assignme

nt

Yule’s coefficient

of colligation

04 July II 04 Central and

noncentral

moments and

their

interrelationships,

sheppard’s

corrections

Problem

solving

July 11 th

World

populatio

n day

celebratio

n

05 July III 04 Measures of

skewness based

on quartiles and

moments

Problem

solving

Assignme

nt

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

Assignme

nt

11 Sept ember I 04 Distribution

functionfor both

discrete and

continuous r.v

II internal

exams

12 September II 04 Mathematical

expectation,defini

tion statement of

its basic results

and some simple

problems

Problem

solving

13 September III 04 Revision for slow

learners

14 September IV 04 revision


syllabus


question papers


end

examinati

ons

18 October IV 04 ,,


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

Name of the Module : Statistical Methods-II





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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

Assignme

nt

03 November III 04 Normal,

Exponential

distributions

Problem

solving

Assignme

nt

04 November IV 04 Interpolation,

Methods of

interpolation,

Graphic method

Problem

solving

Assignme

nt

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

Assignme

nt

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 revision


15 February III 04 practicals

16 February IV 04 practicals

17 March I 04 Revision of the

syllabus

18 March II 04 Solving the old

question papers

,,

19 March III 04 Semester

end

examinati

ons


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

Name of the Module : Statistical Quality Control (P-IV)





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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 09

05 July II 04

06 July III Pushkara

Holidays 14th to

25th

07 July IV 08

O8 August I 10

09 August II 07

10 August III 05 First

Internal

Exams

11 August IV 11

12 Sept ember I 04

13 September II 04

14 September III 04

15 September IV 04


syllabus

Second

Internal

Exams


question papers

18 October III Dasara

Holidays

19 October IV ,,

Semester

end

examinati

ons

20 November I ,,,,,,,,


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

Name of the Module : Sampling Techniques and Design of Experiments





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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 ……

11

January III 04 Unit test-1 II internal

exam

12 January IV 04 revision

13 February I 04 Project

work


15 March I 04 Revision

16 March II 04 Revision

17 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-II





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

Remarks

01 June III 04 Vital statistics,

registration

method, census

method

02 June IV 04 Mortality rates Problem

solving

Assignme

nt

03 July I 04 Fertility rates Problem

solving

Assignme

nt

04 July II 04 Time series-

components

determination of

trendby graphical

and semi averages

method

Problem

solving

July 11 th

World

populatio

n day

celebratio

n

05 July III 04 Least squares and

moving average

methods

Problem

solving

Assignme

nt

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

Assignme

nt

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 Revision


question papers


end

examinati

ons

18 October IV 04 ,,


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

Name of the Module : Sampling Techniques and Design of Experiments-II





of hrs

Topic Curricul

ar

activity

Co-

curricular

activity

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 CRD

10 January II RBD

11

January III 04 LSD II internal

exam

12 January IV 04 22 experiment

13 February I 04 23 experiment Project

work


15 March I 04 Revision

16 March II 04 Revision

17 March III 04 Revision

18 March IV 04 Semester

end xams

GOVERNMENT COLLEGE (A) : RAJAHMUNDRY B.A I Year...

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