deyartment statisitics statktics o exarnination

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$Si tsrieftiliiBHAVAN'S VIVEKANANDA COLLEGE OF SCIENCE, HUMANITIES AND COMMERCE

(Accredited with 'A' Grade by NAAC)

Autonomous College & Affiliated to Osmania University

Deyartment of Svlatftematics ilnd Statisitics

ts.Sc Statktics Sy ffabus and Scheme o Exarnination

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Assessment

Exam

HRs /WEEK

Durationof

Semister

Exam

lnternalMarks

External

Marks

Total

MarkscreditsYEAR SEM PAPER TITLE OF THE PAPER

4 30 70 100 4I Theory sf722Descriptive Statistics and

Probability

2 15 35 IlPractical sfL22PDescriptive Statistics and

Probability Practical

sr222 Probability Distributions 4 3 30 70 100 4ll Theory

2 15 35 50 L

I

illl Practical sr222P

Probability DistributionsPractical

3

4 3 4lll Theory sT322Statistical Methods and

lnferene I

1

Iillll Practical sT322P

Statistical Methods and

lnferene I Practical2 3 15 35 50

lV Theory sr422 Statistical lnferene ll 4 30 100 4

IVlV Practical sr422P Statistical lnferene ll Practical 2 15 3s 1

V Theory sT522 Applied Statistics I 3 30 70 100 3

Statistical Quality Control and

Reliability3 3 30 70 3

V Practical sT5 22 P Applied Statistics I Practical 2 3 15 35 50 1

V

VA Practical ST522APStatistical Quality Control and

Reliability Practical2 3 15 35 50 l

Vl Theory 5T622 Applied Statistics ll 3 3 30 70 100 3

V1A Theory sT622A Operation Research 3 3 30 70 100 3

Vl Practical sr622P Applied Statistics ll Practical 2 3 15 35 50 1

ilt

VI

VIA Practical sf622AP Operation Research Practical 2 3 15 35 50 I

TotalI

44 48 350 840 L200 36

6SL lill- f

CODE

3

50I

3

70 10030

3 70I

50

3

VA Theory sT522A 100

@tsHrvi{hCode: ST122

UNIT _I

Introduction: lmportance of statistics, concepts of statistical population and a sample -quantitative and qualitative data - collection of primary and secondary data. Measurement scales-

nominal, ordinal, interval and ratio. Classification and tabulation of data. Construction ofunivariate and bivariate frequency distributions. Diagrammatic and graphical representation ofdata. Designing a questionnaire and a schedule.

l5LUNIT-II

Descriptive Statistics: Measures of central tendency (mean, median, mode, geometric mean andharmonic mean) with simple applications. Absolute and relative measures of dispersion (range,quartile deviation, mean deviation and standard deviation) with simple applications.

Moments - lmportance of moments, central and non-central moments, and theirintenelationships, Sheppard's corrections for moments for grouped data. Measures of skewnessbased on quartiles and moments and kurtosis based on moments with real life examples.

15LUNIT-III

Random Variables: Definition of random variable, discrete and continuous random variables,functions of random variables, probability mass function and probability density function withillustrations and expectation of a random variable and basic theorems of expectation.Distribution function and its properties. Transformation of one-dimensional random variable(simple I -1 functions only). Definition of moment generating function (m.g.f), cumulantgenerating function (c.g.l), probability generating function (p.g.f) and characteristic function (c.f)and statements of their properties with applications. Chebyshev,s , and Cauchy-schwartz,sinequalities and their applications.

l5LPage I I

l"v N,6ll es Ir/Board of Stu

in Statis tlcs O tJ0 6f1,rr

Bhavan's Vivekananda College of Science, Humanities & CommerceAccredited with 'A' grade by NAAC

Autonomous College(Affiliated to Osmania University)

B.Sc. I Year I Semester: Statistics Syllabus(Examination at the end of I Semester) 60 hrs

Paper-I : Descriptive Statistics & Probability (4 hrs/week)

Probability: Basic concepts in probability--{eterministic and random experiments, trail, outcome,sample space, event, and operations ofevents, mutually exclusive and exhaustive events, and equallylikety and favorable outcomes with examples. Mathematical, statistical and axiomatic definitions ofprobability with merits and demerits. Conditional probability and and Independent events. Additionand multiplication theorem for n events. Boole's inequality and Bayes' Theorem - numericalproblems

15L

UNIT.IV

Y

l. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand &Sons,New

Delhi.

2. S.P.Gupta, (2001). Statistical Methods, Sultan Chand & Sons, New Delhi.

3. Dr.M.Jagan Mohan Rao and Papa Rao:A Text book of statistics paperJ, Deepthi

publication.

List of Reference Books:

l. William Feller: Introduction to Probability theory and its applications. Volume- I,Wiley

2. GoonAM,Gupta and Das Gupta B: Fundamentas of Statistics,Vol-l,the World press

pvt.Ltd.,Kolkota

3. Hoel P.G: lntroduction to Mathematical Statistics, Asia Publishing house.

4. Dr M Jagan Mohan Rao, Dr N Srinivasa Rao, Dr Padi Tirupathi Rao and Smt D. Vijaya

Lakshmi, BSc Statistics I Year , Telugu Academy

5. Sanjay Arora and Bansi Lal:New mathematical Statistics: Satya Prakashan,New Delhi

6. Hogg,Tanis,Rao:Probability and Statistical Inference.T th edition.Pearson.

7. Statistics for Management - Levin & Rubin

8. B.L. Agarwal, Programmed Statistics, New Age Intemational, 2007.

9. Gerald Keller : Applied Statistics with Microsoft excel . Duxbury, Thomson Leaming.

10. 12. Levine, Stephen, Krehbiel, Berenson: Statistics for Managers using Microsoft Excelth

4 edition. Pearson Publication.

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Text Books:

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@fiiiivi{hBhavan's Vivekananda College of Science, Humanities & Commerce

Accredited with 'A' grade by NAACAutonomous College

(Affiliated to Osmania University)B.Sc. IYearlSemester

Paper - I - Statistics Practical Syllabus

la. Computation of Measures of Central tendency for raw data.

lb. Computation of Measures of Central tendency for Raw data Using MS Excel.

2a. Computation of Measures ofCentral tendency for discrete and continuous data.

2b. Computation of Measures of Central tendency for discrete and continuous data

using MS Excel

3a. Computation of Measures ofdispersion for raw data.

3b. Computation of Measures of dispersion for Raw data Using MS Excel.

4a. Computation of Measures ofdispersion for discrete and continuous data.

4b. Computation of Measures of dispersion for discrete and continuous data

using MS Excel

5a. Graphical Presentation of data (Histogram, Frequency polygon, Ogives)

5b. Graphical Presentation of data (Histogram, Frequency polygon, Ogives) using MS

Excel

6a. Diagrammatic Presentation of data (Bar, Ste.m & leaf, Box plot and Pie).

6b. Diagrammatic Presentation of data (Bar, and Pie) using MS Excel

7. Computation ofnon-central and central moments - Sheppard's conection for grouped

data.

8a. Computation ofco-efficient of Skewness and Kurtosis - Karl Pearson's and Bowley's p1

and P2.

8b. Computation of co-efficient of Skewness and Kurtosis - Karl Pearson's and

Bowley's p| and pu using MS Excel

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@ts}ifi''tiiiBhavan's Vivekananda College of Science, Humanities & Commerce

Accredited with 'A' grade bY NAACAutonomous College

(Affiliated to Osmania University)B.Sc. I Year II Semester: Statistics Syllabus

(Examination at the end ofII Semester) 60 hrsPaper- II : Probability Distributions (4 hrs/ rysok)

UNIT - I

Bivariate Random variables: Notion of bivariate random variable, bivariate distribution and

statement of its properties. Joint, marginal and conditional distributions. Independence ofrandom variables. Statement and applications ofweak law of large numbers and central limittheorem for identically and independently distributed (i.i.d) random variables with finitevariance.

l5LUNIT - II

Discrete distributions: Uniform, Bemoulli, Binomial, Poisson, Negative binomial, Geometricand Hyper-geometric(mean and variance only) distributions. Propefties of these distributionssuch as m.g.f ,c.9.f., p.g.f., c.f., and moments up to fourth order and their real life applications.Reproductive property wherever exists. Binomial approximation to Hyper-geometric, Poissonapproximation to Binomial and Negative binomial distributions.

t6L

UNIT -III

14L

UNIT _ IV

Continuous distributions (Continued): Exponential, Gamma, Beta of two kinds (mean andvariance only) and Cauchy (definition and c.f. only) distributions. Properties of thesedistributions such as m.g.f., c.g.f., c.f., and moments up to fourth order, their real lifeapplications and reproductive productive property wherever exists.

15L

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Continuous distributions: Rectangular and Normal distributions. Importance of Normaldistribution. Normal distribution as a limiting case of Binomial and Poisson distributions.Properties ofthese distributions such as m.g.f, p.g.f, c.g.l c.f., and moments up to fourthorder ,their real life applications. Weibul distribution - computation of its mean and variance.

V

Text Books:

l. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand

&Sons,New Delhi.


3. Dr.M.Jagan Mohan Rao and Papa Rao:A Text book of statistics paper-I, Deepthi

publication.

List of Refe nce Books:

l. William Feller: Introduction to Probability theory and its applications. Volume-

I,Wiley

2. GoonAM,Gupta and Das Gupta B:Fundamentas of Statistics,Vol-l,the World press

pvt.Ltd.,Kolkota

3. Hoel P.G:Introduction to Mathematical Statistics, Asia Publishing house.

4. Dr M Jagan Mohan Rao, Dr N Srinivasa Rao, Dr Padi Tirupathi Rao and Smt D. Vijaya

Lakshmi, BSc Statistics I Year , Telugu Academy

5. Sanjay Arora and Bansi Lal:New mathematical Statistics: Satya Prakashan,New

Delhi

6. Hogg,Tanis,Rao:Probability and Statistical lnference.T th edition.Pearson.

7. Statistics for B.Sc I year, Telugu Academy.

8. Sambhavyata Avadhi Siddantalu-Telugu Academy

9. Sahasambandham-Vibhajana Siddantamulu - Telugu Academy

10. K.V.S. Sarma: statistics Made Simple:do it yourself on PC. PHI

I l. Statistics for Management - Kevin & Rubin

12. Gerald Keller :Applied Statistics with Microsoft excel . Duxbury, Thomson Learning.

13. Levine, Stephen, Krehbiel, Berenson: Statistics for Managers using Microsoft Excel

rh

4 edition. Pearson Publication

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@fiiiivi{iiBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc. I Year II Semester

Paper - II - Statistics Practical Syllabus

Code: ST222P

I a. Fitting of Binomial distribution - Direct Method.

1b. Fitting of Binomial distribution - Direct Method using MS Excel.

2. Fitting of Binomial distribution - Recurrence Relation Method.

3a. Fitting of Poisson distribution - Direct Method.

3b. Fitting of Poisson distribution - Direct Method using MS Excel.

4. Fitting of Poisson distribution - Recunence Relation Method.

5. Fitting of Negative Binomial distribution.

6. Fitting of Geometric distribution.

7. Fitting of Hyper geometric distribution.

8. Fitting of Normal distribution - Areas Method.

9. Fitting of Normal distribution - Ordinates Method.

l0a. Fitting of Exponential distribution.

10b. Fitting of Exponential distribution using MS Excel.

I la. Fitting ofCauchy distribution.

1lb. Fitting of Cauchy distribution using MS Excel.

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Page | 6

@BriHti{hBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc. II year III Semester: Statistics Syllabus

(Examination at the end of III Semester)Paper-III - Statistical Methods & Inference I

T]NIT I

Principle of least squares: Fitting ofa straight line, quadratic, exponential and power curves.Analysis of categorical data. Definition of attributes. Independence, association and partialassociation ofattributes, various measures of association (Yule's) for 2 -way dala and coefficientofcontingency (Pearson and Tcherprow) and coefficient ofcolligation with real life examples.

(15L)

UNIT II

Correlation & Regression: Product moment correlation coefficient and its properties. Bivariatedata, scattered diagram, computation ofcorrelation coefficient for grouped data, Spearman'sRank correlation coefficient and its properties, correlation ratio. Partial and multiple correlationcoefficients (only for three variables). Simple linear regression, lines ofregression, properties ofregression coefficients, correlation verses regression. Regression for 3 variables and coefficientof determination (R2).

0sL)UNIT III

Sampling distribution: Concept - Population, Sample, parameter, statistic, samplingdistribution and standard error and its application. Definitions of exact sampling distributions-statements and properties of chi-square, t and F distributions and their intenelationships.Independence of sample mean and variance in random sampling from normal distributions.

Estimation: Point Estimation - Distinction between Estimator and Estimate - Properties ofEstimators - Concept of Unbiasedness & Consistency, Efficiency and Sufficiency - Statement ofNeyman's Factorization theorem - Simple Applications.

(r4L)

UNIT IV

Methods Of Estimation: Maximum likelihood estimator (MLE) and their properties -MLE problems based on Binomial, Poisson, Exponential, Normal etc. Method of moments -definition and problems based on method of moments.Interval estimation - Concept, Distinction between point estimation and interval estimation -Confidence interval and confidence limits.

Code: ST322

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Text Books:

L V.K.Kapoor and S.C.Gupta :Fundamentals of Mathematical Statistics, Sultan Chand& Sons,New Delhi


3. A. Mohan Rao, N. Srinivasa Rao, R. Sudhakar Reddy and T C Ravichandra KumarStatistical Methods and Inference- Telugu Academy, Hyderabad


l. Wiltiam Feller: Introduction to Probability theory and its applications. Volume-I, Wiley

Publication.

2. Goon AM, Guptamk,Das Gupta B:Fundamentas of Statistics, Vol-ll,the World press

prA. Ltd. ,Kolakota .

3. Hoel P.G: lntroduction to mathematical Statistics, Asia Publishing house.

4. Sanjay Arora and Bansi Lal : New mathematical Statistics: Satya Prakashan, New

Delhi

5. Hogg, Tanis,Rao:Probability and Statistical Inference.Tth edition. Pearson.

6. Hogg and Craig: lntroduction to Mathematical Statistics. Printis Hall

7. Parimal Mukhopadhyay : Mathematical Statistics, New Central Book Agency.

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@Bliirt'iiiiBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc II Year III Semester

Paper-III - Statistics Practical Syllabus

la. Fitting ofa Straight line by the method of least squares.

lb. Fitting of a Straight line by the method of least squares using MS Excel

2a. Fitting of a Parabola by the method of least squares.

2b. Fitting of a Parabola by the method of least squares using MS Excel

3. Fitting ofa Power curve ofthe type y=axb by the method ofleast squares.

4. Fitting ofan Exponential curves ofthe type y:ab*, y:aeb* by the method of least squares.

5a. Computation of Correlation Co-efficient for ungrouped and grouped data.

5b. Computation of Correlation Co-efficient for ungrouped using MS Excel

6. Computation of Multiple and Partial Correlation Co-efficient.

7. Computation of Correlation Ratio.

8a. Computation of Regression lines for ungrouped and grouped data.

8b. Computation of Regression lines for ungrouped using MS Excel.

9a. Computation of Multiple Regression lines for 3 variables.

/9b. Computation of Multiple Regression lines for 3 variables using MS Excel.

l0a. Computation of Coefficient of determination.

10b. Computation of Coefficient of determination using MS Excel.

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B.Sc. II year IV Semester: Statistics Syllabus(Examination at the end of IV Semester)Paper-IV - Statistical Inference II

UNIT I

Hypothesis and General Test Procedures: Concepts of statistical hlpotheses, null and

altemative hypothesis, critical region, two types of errors, level of significance and power of a

test. One and two tailed tests, most powerful test and test function (non-randomized and

randomized).Neyman-Pearson's fundamental lemma for Randomized tests. Examples in case of Binomial,Poisson, Exponential and Normal distributions and their powers. Use of central limit theorem intesting. (lsl)

UNIT II

Large Sample Tests: Large sample tests for attributes and variables; confidence intervals formean(s), proportion(s), standard deviation(s) and correlation coefficient(s). (l5L)

UNIT III

Small Sample Tests: Tests of significance based on 12, t and F. 12+est for goodness of fit andtest for independence of attributes. Definition of order statistics and statement of theirdistributions. (lsl,)

UNIT IV

Non-Parametric Tests: lntroduction to Non Parametric tests - their advantages anddisadvantages, comparison with parametric tests. One sample run test, sign test and Wilcoxon-signed rank tests (single and paired samples). Two independent sample tests: Median test,Wilcoxon -Mann-Whitney U test, Wald Wolfowitz's runs test.

(lsL)

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Page | 10

Text Books:

L V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan

Chand&Sons, New Delhi.


3. A. Mohan Rao, N. Srinivasa Rao, R. Sudhakar Reddy and T C Ravichandra KumarStatistical Methods and Inference- Telugu Academy, Hyderabad

I . 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-ll, 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 :lntroduction to Mathematical statistics. Printis Hall

6. Siegal,S.,and Sidney: Non-param etric statistics for Behavioral Science. McGraw Hill.

7. GibbonsJ.D and Subhabrata Chakraborti: Nonparametric Statistical Inference. Marcel

Dekker.

8. Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.

9. Conover: Practical Nonparametric Statistics. Wiley series.

10. V.K.Rohatgi and A.K.Md.Ehsanes Saleh: An introduction to probability and statistics.

Wiley series.

I l. Mood AM,Graybill FA,Boe's DC. lntroduction to theory of statistics. TMH

12. Paramiteya mariyu aparameteya parikshalu. Telugu Academy.

13. K.V.S. Sarma: Statistics Made simple do it yourself on PC. PHI

14. Gerald Keller: Applied Statistics with Microsoft excel. Duxbury. Thomson Leaming

15. Levin, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft Excel.4th

edition. Pearson Publication.

16. Hogg, Tanis, Rao. Probability and Statistical Inference. 7th edition. Pearson

Publication.

I 7. Milton and Amold(fourth Edition):lntroduction to Probability and statistics,Tata

Mcgraw hill Publication

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Bhavan's Vivekananda College of Science, Humanities & CommerceAccredited with 'A' grade bY NAAC


B.Sc Il Year IV Semester

Paper - IV - Statistics Practical Syllabus

la. Test for Proportions (Single and difference ofproportions in Large Sample).

lb. Test for Proportions (Single and difference of proportions in Large Sample) using

MS Excel.

2a. Test for Means (Single and difference ofmeans in Large Sample).

2b. Test for Means (Single and difference of means in Large Sample) using MS Excel.

3a. Test for variances (Single and difference ofvariances in Large Sample).

3b. Test for variances (Single and difference of variances in Large Sample) using MS

Excel.

4a. Test for Correlation Co- efficient (Large Sample).

4b. Test for Correlation Co- efficient (Large Sample) using MS Excel.

5a. Test for means (Single mean, difference ofmeans and paired observations in Small

Sample).

5b, Test for means (Single mean, difference ofmeans and paired observations in Small

Sample) using MS Excel.

6a. Test for Correlation Co-efficient (Small Sample).

6b. Test for Correlation Co-efficient (Small Sample) using MS Excel.

7a. Test for Single variance (Small Sample).

7b. Test for Single variance (Small Sample) using MS Excel.

8a. Test for difference ofVariances (Small Sample).

8b. Test for difference of Variances (Small Sample) using MS Excel.

9a. 12 - test (independence ofattributes and goodness of fit).

9b. 2g2 - test (independence of attributes and goodness of fit) using MS Excel.

10. NP - Tests for one sample (Run test, Sign test and Wilcoxon signed rank test).

I l. NP - Tests for two samples (Run test, Sign test and Wilcoxon signed rank test).

12. NP - Tests for two independent samples (Median test, Mann - Whitney U-test, Run

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@fiiiit'i{iiBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc. III year V Semester: Statistics Syllabus

(Examination at the end of V Semester)Paper-V - Applied Statistics I

Unit - IDesign of Sample Surveys: - Organization and execution of sample surveys - principle steps insample survey - Pilot survey - sampling and non-sampling errors - advantages of sampling overcomplete census - limitations of sampling.Sampling techniques: Subjective, probability and mixed sampling methods. Simple random

sampting with and without replacement - unbiased estimate of the mean, variance of the estimate

ofthe mean finite population correction estimation ofstandard error from a sample -determination of sample size. Estimates ofpopulation mean, total, and proportion, their variances

and the estimates of variances by Simple Random Sampling with and without replacement(SRSWR and SRSWOR).

(t2L)Unit - II

Stratified random sampling - properties ofthe estimates - unbiased estimates ofthe mean andvariance ofthe estimates ofthe mean-optimum and proportional allocations - relative precisionof a stratified sampling and simple random sampling - estimation of gain in precision in stratifiedsampling.Systematic Random Sampling: Systematic sampling with N : nk. Estimates of population mean,

total, their variances and estimates of variances. Comparison of relative efficiencies and

advantages and disadvantages of above methods of sampling.(t2L)

Unit-mTime series: -Time series and its components with illustrations, additive, multiplicative andmixed models. Determination of trend by least squares, moving average methods.GroMh curves and their fitting with reference to Modified exponential, Gompertz andLogistic curves. Determination ofseasonal indices by Ratio to moving average, ratio to trend andlink relative methods.

(11 L)Unit-IV

Index Numbers: -Concept, construction, uses and limitations of simple and weighted indexnumbers. Weighted Index Number - Laspeyer's, Paasche's, Fisher's, Marshall Edgeworth andKellys index numbers. criterion of a good index numbers (Test of consistency), problemsinvolved in the construction of index numbers. Fisher's index as ideal index number. Fixed andchain base index numbers. Cost of living index numbers and wholesale price index numbers.Base shifting, splicing and deflation of index numbers.

Official Statistics: - Functions and organization of CSO and NSSO. Agricultural Statistics, Areaand yield statistics. National lncome and its computation, utility and difficulties in estimarion ofnational income. (r0 L)

Code: ST522

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Page | 13

Text Books:

l. V.K.Kapoor and S.C.Gupta: Fundamentals of Applied Statistics, Sultan

Chand & Sons, New Delhi.

2. Parimal Mukhopadhyay : Applied Statistics . New Central Book agency. Books and Allied (P)

Limited.

3. B. L. Agarwal: Basic Statistics, New Age International Limited.

List of reference books:

I . Daroga Singh and Chowdhary: Theory and Analysis of Sample survey designs.

Wiley Eastem.

2. M.R.Saluja: Indian Official Statistics. ISI publications.

3. S.P.Gupta : Statistical Methods. Sultan Chand and Sons.

4. K.V.S. Sarma: Statistics made simple : do it yourself on PC. PHI

5.Gerald Keller; Applied Statistics with Microsoft excel. Duxbury. Thomson

Leaming.

6. Levine, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft

Excel. Pearson Publication.

7. Arora, Sumeet Arora,S.Arora: Comprehensive Statistical Methods. S.Chand.

8. A.M.Goon,M.K.Cupta,B.Dasgupta Fundamentals of Statistics Vol II World Press

Private Ltd.,Calcutta

9. A.M.Goon,M.K.Gupta,B.Dasgupta An outline of Statistical Theory Vol II World

Press Private Ltd., Calcuttal T.

10. D.V.L.N. Jogiraju, C. Srikala, Palnati Sudarsan, Applied Statistics, Kalyani Publishers.

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6$tsti?ittih Code: ST522P

Bhavan's Vivekananda College of Science, Humanities & CommerceAffiliated to Osmania UniversitY

Autonomous College(Accredited with 'A' grade by NAAC)

B.Sc III Year V Semester 45 hrsPaper-V - Statistics Practical Syllabus (2 h,s/ weel (3 hrs/ week)

Sampling Theory

l. Estimation of Population ofmean, Population Total, Variance ofthese estimates by

Simple Random Sampling with and without replacement and their comparison.

2. Stratified Random Sampling with Proportioritnd Optimum allocations, Comparison

between Proportional and Optimum allocation with SRSWOR.

3. Systematic Sampling with N:nk, Comparisons of systematic sampling with stratifiedsamPling and sRSwoR

rime Series4a. Measurement oftrend by the method of moving averages.

4b. Measurement of trend by the method of moving averages using MS Excel.

5a. Measurement of trend by the method of least squares.

5b. Measurement of trend by the method of least squares using MS Excel.

6a. Measurement of seasonal indices by Ratio to trend Method.

6b. Measurement of seasonal indices by Ratio to trend Method using MS Excel.

7a. Measurement ofseasonal indices by Ratio to moving averages.

7b. Measurement of seasonal indices by Ratio to moving averages using MS Excel.

8a. Measurement ofseasonal indices by Link Relative method.

8b. Measurement of seasonal indices by Link Relative method using MS Excel.

Index Numbers9a.Computation ofLaaspayer's, Paasche's, Fisher's, Marshall Edgeworth and Kelly's Price

and Quantity Index Numbers.

9b. Computation of Laaspayer's, Paasche's, Fisher's, Marshall Edgeworth and Kelly's

Price and Quantity Index Numbers using MS Excel.

l0a. Computation of Time Reversal Test, Factor Reversal Test and Circular Test.

l0b. Computation of Time Reversal Test, Factor Reversal Test and Circular Test using

MS Excel.

\i t}0f,Construction of Cost of Living Index Numbers.

.,rxj0d Con.t.uction of Cost of Living Index Numbers using MS Excel.

,2.*l* Base Shifting and Splicing of In ex Numbers

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Board of st lo!ln Statisr lcs

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Page | 15

@fiiirti{iiBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc. III year V Semester: Statistics Syllabus

(Examination at the end of V Semester)

PapeT.VA - STATISTICAL QUALITY CONTROL & RELIABILITY

UNIT _ IStatistical Quality Control:lmportance of SQC in industry. Statistical basis of Shewart control charts. Construction ofcontrol charts for variables (mean, range and standard deviation) and attributes ( p , np, and c-

charts with fixed and varying sample sizes). Interpretation of control charts. Natural tolerancelimits and specification limits, process capability index.

(l3L)

UNIT - II

Acceptance sampling plans: Concept of AQL and LTPD. Producers risk and consumer's riskSingle and Double sampling plans for attributes and their OC and ASN functions. Design ofsingle and double sampling plans for attributes using Binomial and Poisson distributions.

(12 L)

UNIT III

Six Sigma: Six sigma- Overview, Foundations and principles of Six Sigma, Roles andresponsibilities in Six Sigma Implementation, DMAIC / DMDAV methodology, Design for SixSigma. Natural tolerance limits and specification limits, process capability index.

(10 L)

UNIT IV

Reliability: Introduction. Hazard function, Exponential distribution as life model, its memory-less property. Reliability function and its estimation. System reliability - series, parallel and k outof n systems and their reliabilities

(10 L)

Code: ST522A

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Text Books:

I . V.K.Kapoor and S.C.Gupta: Fundamentals of Applied Statistics, Sultan

Chand & Sons, New Delhi

2. D.C.Montgomery: lntroduction to Statistical Quality Control, John Wiley & Son 2009.

List of reference books :

l. S.K.Sinha: Reliability and life testing. Wiley Eastem

2. L.S.Srinath: Reliability Engineering. Affi liated East-West Press.

3. S.M.Ross: Probability Models. Harcourt lndia PVT.Ltd.,

4. Parimal Mukhopadhyay : Applied Statistics. New Central Book agency

5. Anuvartita Sankhyaka sastram - Telugu Academy.

6. R.C.Cupta: Statistical Quality Control. Published by Khanna Publishers

7. Parikriya Parishodhana - Telugu Academy.

8. A.M.Goon,M.K.Cupta,B.Dasgupta Fundamentals of Statistics Vol II World Press


9. A.M.Goon,M.K.Gupta,B.Dasgupta An outline of Statistical Theory Vol II Wortd

Press Private Ltd., Calcutta 17.

10. D.V.L.N Jogiraju, C. Srikala, K. Ravi Kumar Quality, Reliability and Operation Reaserch,

Kalyani Publishers.

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Page I 17

@fiiiffi{hBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc III Year VI Semester

Affiliated to Osmania UniversityPaper-VA- Statistics Practical Syllabus

Statistical QualiW Control

Code: ST522AP

(2 hrs, wesk)

of X-bar and R Chart.

of X-bar Charl and R Chart using MS Excel.

of X-bar and Standard deviation cha(.

ofX-bar and Standard deviation chart using MS Excel.

of p, np - charts with fixed and varying sample sizes.

of p, np - charts with fixed and varying sample sizes using MS Excel.

ofc - charts.

of C- Charts using MS Excel.

of u - charts.

of u - charts using MS Excel.

I a. Construction

lb. Construction

3a. Construction

3b. Construction

4a. Construction

4b. Construction

5a. Construction

5b. Construction

6a. Construction

6a. Construction

Acceptance Sampling Plans

7a. Designing a single sampling plan and construction of its OC and AOQ curves.

7b. Construction of Single Sampling Plan - OC and AOQ Curve using MS Excel.

8a. Designing a double sampling plan and construction of its ASN curve.

8b. Construction of Double Sampling Plan - OC and ASN Curve using MS Excel.

9. Problems on Hazard rate, Series, Parallel and K out ofn System.

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Page I l8

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B.Sc. III year VI Semester: Statistics Syllabus(Examination at the end of VI Semester)

Paper-VI- Applied Statistics II

UNIT I

Analysis of Variance - ANOVAConcept of Gauss-Markov linear model with examples, statement of Cochran's theorem,ANOVA - one-way, two-way classifications with one observation per cell. Expectation ofvarious sums of squares and their Statistical analysis.

(r2 L)UNIT II

Design of ExperimentsImportance and applications of design of experiments. Principles of experimentation.Analysis of Completely randomized Design (C.R.D), Randomized Block Design (R.B.D) and

Latin Square Design (L.S.D) including one missing observation, expectation of various sum ofsquares. Comparison ofthe efficiencies ofthe above designs.

(12 L)UNIT III

Vital statistics: Introduction, definition and uses of vital statistics. Sources of vital statistics,registration method and census method. Rates and ratios, Crude death rates, age specific deathrate, standardized death rates, crude birth rate, age specific fertility rate, general fertility rate,total fertility rate. Measurement ofpopulation growth, crude rate ofnatural increase- Pearl's vitalindex. Gross reproductive rates and Net reproductive rate, Life tables, construction and uses oflife tables and Abridged life tables.

(11L)UNIT IV

Demand Analysis: Introduction. Demand and supply, price elasticity of supply and demand.Methods of determining demand and supply curves, Leontiff s ,Pigous's methods of determiningdemand curve from time series data, limitations of these methods. Pareto law of incomedistribution, curves of concentration.

(10 L)

Code: 5T622

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Text Books:

l. V.K.Kapoor and S.C.Gupta: Fundamentals of Applied Statistics, SultanChand & Sons, New Delhi.

2. Parimal Mukhopadhyay : Applied Statistics . New Central Book agency. Books and Allied (P)

Limited.

3. B. L. Agarwal: Basic Statistics, New Age International Limited

List of reference books:

l. Daroga Singh and Chowdhary: Theory and Analysis of Sample survey designs.

Wiley Eastem.

2. M.R.Saluja: Indian Official Statistics. ISI publications.

3. S.P.Gupta : Statistical Methods. Sultan Chand and Sons.

4. Pratirupa Sidhanthamulu - Telugu Academy.

5. Prayoga Rachana and Visleshana - Telugu Academy.

6. K.V.S. Sarma: Statistics made simple : do it yourself on PC. PHI

7. Gerald Keller; Applied Statistics with Microsoft excel. Duxbury. Thomson

Leaming.

8. Levine, Stephan, Krehbiel, Berenson: Statistics for Managers using Microsoft

Excel. Pearson Publication..


10. Arora, Sumeet Arora,S.Arora: Comprehensive Statistical Methods. S.Chand.

I l. A.M.Goon,M.K.Gupta,B.Dasgupta Fundamentals of Statistics Vol II World Press



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@fiiHviih Code: ST622



B.Sc III Year VI SemesterPaper-VI - Statistics Practical Syllabus

(2 hrs/ weok)

Design of Expe riments

la. ANOVA of One Way Classification.

I b. ANOVA of One Way Classification using MS Excel.

2a. ANOVA of Two Way Classification.

2b. ANOVA of Two Way Classification using MS Excel.

3a.ANOVA of Completely Randomized Design.

1 Ib. ANOVA of Completely Randomized Design using MS Excel.

, 7a. ANOVA of Randomized Block Design and Estimation of one missing value in RBD.

i 2b. ANOVA of Randomized Block Design using MS Excel.

; 3. ANOVA of Latin Square Design and Estimation of one missing value in LSD.

Vital Statistics

4.'Computation of various Mortality Rates, Ferlility Rates and Reproduction Rates.

i 5h.Construction of Complete t-ife Tables.

5b. Construction of Complete Life Tables using MS Excel.

Demand Analysis

6i Fitting of Pareto's curve.

7e. Fitting of Lorenz Curve.

ZU. fitting of Lorenz Cune using MS Excel.

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@fiiiiviiiiBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc. III year VI Semester: Statistics Syllabus

(Examination at the end of VI Semester)Paper VIA - O.R.

UNIT - ILinear Programming: Introduction to OR, Convex sets and their properties, Nature, Scope,

Functions, Linear programming problem - Formulation of LPP - Solving the LPP by graphical

method. Fundamental theorem of LPP (only statement). Solving the LPP by simplex method,

Two- phase simplex method.(13 L)

UNIT II

Big - M Method: Solution to LPP using Big-M method (Penalty Method) and Concept ofdegeneracy and resolving it.

Duality: Concept ofduality, duality as LPP. Dual-Primal relationship.

Sequencing:Processing n Jobs through 2 and 3 Machines & 2 Jobs through m Machines.

(r2L)

UNIT - III

Transportation Problem: Definition of transportation problem, TPP as a special case of LPP,Initial basic feasible solutions by North-West Corner Rule, Matrix minimum methods and VAM.Optimal solution through MODI method and stepping stone method for balanced and unbalancedTransportation problem. Maximization TP. Degeneracy in TP and resolving it. Concept ofTransshipment problem.

(r0 L)UNIT IV

U nbalanced problems. Travelling Salesman Problem

Code: 5T622A

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Assignment Problem: Concept. Mathematical Formulation. Assignment problem as special caseof TP and LPP Solution. Optimal solution using Hungarian method for Balanced and

Text books:

l. Kanti Swaroop, P.K.Gupta and ManMohan: Operations Research. Sultan Chand.

2. Operation Research - S D Sharma

3. Taha : Operations Research: An lntroduction : Mac Millan.

l. Gass: Linear Programming. McGraw Hill.

2. Hadly : Linrar programming. Addison-Wesley.

3.Wayne L. Winston : Operations Research. Thomson, India edition.4th edition.


5. Parikriya Parishodhana - Telugu Academy.


Press Private Ltd.,Calcuna1 7.

7. D.V.L.N Jogiraju, C. Srikala, K. Ravi Kumar Quality, Reliability and Operation Reaserch,

Kalyani Publishers.

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List of reference books :

Page | 23

@tslliii'ahBhavan's Vivekananda College of Science, Humanities & Commerce


(Affiliated to Osmania University)B.Sc III Year VI Semester

Paper-VI A- Statistics Practical Syllabus (2 hrs/ weok)

la. Solution of L.P.P. by graphical method.

lb. Solution of L.P.P. by graphical method using TORA.

2a. Solution of L.P.P. by Big-M method.

2b. Solution of L.P.P. by Big-M method using TORA.

3a. Solution of L.P.P. by Two-phase method.

3b. Solution of L.P.P. by Two-phase method using TORA.

4. Solution of L.P.P by Duality.

5a. Determination of optimum solution to T.P. using MODI algorithm.

5b. Determination of optimum solution to T.P. using MODI algorithm using TORA.

6. Determination of optimum solution to Traveling salesman problem.

7a. Determination of optimum assignment cost to Assignment problem (Balanced and

Unbalanced) for all cases.

7b. Determination of optimum assignment cost to Assignment problem (Balanced

and Unbalanced) for all cases using TORA.

8. Problems of n jobs on 2 Machines.

9. Problems of n jobs on 3 Machines.

10. Problems of n jobs on m Machines.

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Code: ST622AP

Code No: ST122

-"Jrfiffi€ifiBHAVAN'S VIVEKANANDA COLLEGE OF SCIENCE, HUMANITIES AND COMMERCE

(Accredited with A grade by NAAC)Autonomous College and Affiliated to Osmania University

B.Sc lYear lSemester: End Semester Examination, Nov 2015

Paper: Descriptive Statistics and ProbabilityTime: 3 Hours Max. Marks: 70

1)

2l3)

4ls)E,'

7l8)

9. a)

b)

10. a)

b)

11. a)

b)

L2. al

b)

Note: Scientific calculators are allowed.PART A

Answer any 5 from the following questions

PART B

Answer ALL the Questions

UNIT I

OR

UNIT II

OR

UNIT III

OR

UNIT IV

OR

(5X 3 = 18 Marks)

(13X 4 = 52 Marks)

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Code No: ST122

,{'It Blihv$fi;BHAVAN'S VIVEKANANDA COLLEGE

OF SCIENCE, HUMANITIES AND COMMERCEAccredited with 'A' grade by NAAC

Autonomous College(Afliliated to Osmania University)

B.Sc lYear I Semester: Model paper of End Semester Examination

Pa per: Descriptive Statistics and Probability

Time: 3 Hours Max. Marks: 70

Note: Scientific calculators are allowed.

PART A

Answer any 6 from the following questions (6 X 3 = 18 Marks)

1) Define (i) Nominal Scale (ii) Ordinal scale.

2) Define Classification of data.3) State the properties of a good average.

4) Write about Sheppard's Corrections for moments.

5) lf a card is drawn from a well shuffled pack of cards what is the probability that theselected card is King or Spade.

5) For any two events A and B defined on the sample space S, show thatP(Au B) = P(B) - P (AnB)

7) Define Mathematical Expectation of a random variable.

8) Define M.G.F. and state its properties.PART B

Answer ALL the questions (13 X 4 = 52 Marks)UNIT I

9. a) Explain the various methods of Primary and Secondary data collection.OR

b) Explain the different types of diagrammatic representation of data.UNIT II

10. a) Explain different measures of central tendencies. Discuss their merits and demerits.OR

b) Define moments. Express first four moments in terms of moments about the Origin.UNIT III

11. a) i) State and prove addition theorem of probability for n events.ii) From a city population, the probability of selecting (a) a male or a Smoker is 7/10 (b) a maleSmoker is 2 / 5 and (c) a male, if a Smoker is already selected is 2 / 3. Find the probability of selectinga Smoker, if a male is first selected.

OR

b) i) State and prove Bayes theorem?ii) There are 10 urns of which three contain lwhite and 9 black balls each, other three contains 9

white and 1 black balls each and the remaining four contain 5 white and 5 black balls each. Oneof the urns is selected at random and a ball is taken from it. lt turns out to be white. What is theprobability that (i) an urn containing l white and 9 black balls (ii) urn containing 5 white and 5

black balls was selected?UNIT IV

12. a) i) Define distribution function and state and prove its properties.ii) Define PGF. Also find its mean and variance.

OR

b) State and prove Tschebychev's inequality. A discrete random variable takes values 3,4,5with probabilities 7/2, L/6, and 1/3 resp. Evaluate P lx-u ls3o).

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Code No: ST122

f.,rlfiiHtlrifiBHAVAN'S VIVEKANANDA COLLEGE OF SCIENCE, HUMANITIES AND COMMERCE


B.Sc lYear lSemester: End Semester Examination, Nov 2015Model lnternal Question Paper

Paper: Descriptive Statistics and ProbabilityTime: 1 1,/2Hours Max. Marks: 30

2t.22.23.24.25.

7

2

3

45

6

7

8

9

Multiple Choice Questions

Fill in the blanks

72.13.

14.15.

L6,L7,

18.

19.

20.

Answer all the Questions

PART A

PART B

ll0X%= 5 Marks)

ILOX%= 5 Marks)

(5X3=15Marks)

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Code No: ST122

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Time: 1 7/2HoursPART A

Multiple Choice Questions ILOX%= 5 Marks)

l. Statistics is applied ina) Economics b) Business Management c) Commerce and industry d) All these

2. Data collected on religion from the census reports are

a) Primary data b) Secondary data c) Sample data d) (a) or (b)3. In tabulation source ofthe dat4 ifany, is shown in the

a) Body b) Foot note c) Stub d) Caption4. Which ofthe following results hold for a set ofdistinct positive observations?

a)AM>GM>HM b)HM>GM>AM c)AM>GM>HM d)GM>AM>HM5. If the SD of x is 3, what is the Variance of(5-2x)?

a)6 b)36 c) -l d) 96. l0'h Percentile is equal to

a) l'' decile b) lO'h decile c) 9'h decile d) None of these

7. IfP(A n B ) = 0, then the two events A and B area) Equally likely b) Exhaustive c) Mutually Exclusive d) Independent

8. If p : q are the odds in favour ofan event, then the probability ofthat event is _a)plC b)p/(p+q) c)q/(q+p) d) None ofthese

9. IfX is a random variable which can take only non-negative values, thena) E(x'?) = [E(x)'? b) E(x'?) u E(x)]'? c) E(x'?) s [E(x)]'? d) E(x'?) < [E(x)]':

'10. IfX is a random variable , E(t') is known as

a) CF b) MGF c) PGF d) all the above)

Fill in the blanksI l. Data obtained by conducting a survev is called

ILOX% = 5 Marks)data.

12. The difference between the upper and lower limit of a class is known as

13. Frequency polygon can be drawn with the help of14. lf the AM and HM for two numbers are 5 and 3.2 respectively then the GM will beI 5. For a symmetric distribution coefficient of skewness is

16. IfA and B are two events, the P (A l-1 B ) is17. IfA and B are independent, then P ( A/B )I 8. The set of all outcomes of a random expt is called19. A random variable x has the following pdff(x) = kx,0< X< 2, then k20. The sum ofprobability mass function is equal to

(5X3=15Marks)

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BHAVAN'S VIVEKANANDA COLLEGE OF SCIENCE, HUMANITIES AND COMMERCE(Accredited with A grade by NAAC)

Autonomous College and Affiliated to Osmania UniversityB.Sc lYear lSemester: End Semester Examination, Nov 2015

Model lnternal Question Paper

Paper: Descriptive Statistics and ProbabilityMax. Marks: 30

PART B

Answer all the Questions21. What is meant by qualitative data?22. Define Skewness and Kunosis?23. What do you mean by Mutually Exclusive events?24. Define mathematical expectation ofarandom variable.25. Define the moment generating function ofthe random variable.

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Code No: Sf722P

',*tsIihil€ilfiBHAVAN'S VIVEKANANDA COLLEGE OF SCIENCE, HUMANITIES AND COMMERCE


B.Sc lYear I Semester: Practical End Semester Examination, Nov 2015

Paper: Descriptive Statistics and ProbabilityTime: 3 Hours Max. Marks: 30+5+L5

1)

2l

3)

4l

s)

6)

Note: Scientific calculators are allowed

Part A (Manual)

Answer any 3 from the following questions

Note: 15 Marks Exam based on MS Excel

(3 x 10 =30 Marks)

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BHAVAN'S VIVEKANANDA COLLEGEOF SCIENCE, HUMANITIES AND COMMERCE

(Accredited with A grade bY NAAC)Autonomous College

Affiliated To Osmania University

DEPARTMENT OF STATISTICS

LIST OF EXTERNAL EXAMINERS

NAME COLLEGE PHONE NO.

I Dr. Ch. YugandharSt. Francies Degree college for

Women9849651251

2 Mr. G. Govardhan 984801984s

3 Nrupathunga Degree college 9849621263

1 Mrs. Rama Devi Sujatha Degree college For Women 9908019440

5 Mrs.L.Rajini Koti Women's Degree college 9032822116

6 Mrs. V.Sai Sri Kishore St. Ann's Degree college,Mehdipatnam 9908277382

7 Mr. Venugopal Avanti Degree College 9492543935

8 Mr. Venkata Ramana Jagruti Degree college 949031341I

9 Mrs. Parimala 988s128667

10 Dr. Lavanya AMS Degree College 9948470727

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MNR Degree college, Kukatpally

Mr. Raghavendra Kulkarni

Aurora Degree College

deyartment statisitics statktics o exarnination

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