## WELCOME TO STATISTICS DEPARTMENT

Before 1981, the College operated on departmental basis and by that time there were Department of Mathematics and Science Department of Civil Engineering and so on. In 1981, the schools system commenced with five Schools including School of Science and Technology under which was the Department. Physics and Mathematics, Statistics was then introduced in this department as a programme with mathematical bias-admitting Students with only a minimum of five credits at O’levels including mathematics and economics.

In 1984/85 Session, in accordance with the NBTE’S regulation, the name of the Department was changed to Department of Physical and Mathematical Sciences. Also, when in 1985/86 Session Computer Science was introduced into the department as a programme, the name was again changed to Department of Mathematics and Computer Science to reflect the status. Again in 1989, the department of Computer Science was carved out of the department and the name became department of Mathematics and Statistics. The Department was later split into two in 2005 into Department of Mathematics and Department of Statistics. The Statistics Department of Yaba College of Technology offers courses leading to the award of National Diploma (ND) Full-Time and Part-Time Programmes in Statistics. The full-time programmes last for a minimum of 2 years and a maximum of four years while part-time programmes last for a minimum of three years and a maximum of six years. The pioneer HND graduates in Statistics graduates in Statistics graduated in 1988 from the department.

**Mr. G.O. Lawal,**

**HOD of Statistics**

**PROGRAMMES AND ADMISSION REQUIREMENTS IN STATISTICS**

**HIGHER NATIONAL DIPLOMA IN STATISTICS**

**GOALS AND OBJECTIVES**

The Higher National Diploma Programme in Statistics is designed to produce Statisticians capable of collecting data, analysing and making inference.

The Higher National Diploma Programme in Statistics is a post National Diploma, two year programme aimed at producing professional statisticians. The programme is designed to give the students:

- A thorough knowledge of statistics and statistical methods.
- A deep understanding of statistics and its application within the commercial industrial and scientific environment:
- Practical skills in research methodology, analysis and design of experiments leading to decision making and/or making prediction.
- Ability to use a computer when the need arises;
- Development of their ability to think logically, organize their thought well and communicate such thoughts clearly so that diploma holders of the programme will be able to work in research centres; government establishments; industries and commercial houses as statisticians.
- Set up a statistical project without supervision.

**ENTRY REQUIREMENT**

The entry requirement into Higher National Diploma Programme in Statistics is at least lower Credit grade in National Diploma in Statistics obtained from an accredited statistics programme with one year supervised industrial Experience. In exceptional cases at least two years Industrial experience for candidates with Pass grade or any other equivalent certificate.

**CURRICULUM**

The curriculum of the HND Programme consists of three main components. These are:

(a) General Studies/Education

(b) Foundation Courses

(c) Professional Courses

The General Studies/Education component shall include compulsory courses in English Language and Communication and Social Studies – Citizenship (The Nigeria Constitution). The General Education Component shall account for not more than 10% of total contact hours or the programme.

**Foundation Courses** – Courses in Mathematics and Computer studies. The number of hours will vary with the programme and may account for about 10 – 15% of the total contact hours.

**Professional Courses** – Courses which give the student the theory and practical skills he needs to practice his field of calling at the technician/technologist level. These may account for between 60 – 70% of the contact hours depending on programme.

**CURRICULUM STRUCTURE **

The structure of the HND Programme consists of four semesters of classroom, laboratory and workshop activities in the college. Each semester shall be of 17 weeks duration made up as follows:

15 contact weeks of teaching, i.e. lecture and practical exercises, etc and 2 weeks for tests, quizzes, examinations and registration.

**CONDITIONS FOR THE AWARD OF THE**

Institutions offer accredited programmes for the award of the award of the Higher National Diploma to candidates who successfully complete the programme after passing prescribed course work, examinations and project. Such candidates should have completed a minimum of between 90% and 100% of credit units depending on the programme. Higher Diplomas shall be awarded based on the following classifications:

Distinction – CGPA 3.50 – 4.0

Upper Credit – CGPA 3.00 – 3.49

Lower Credit – CGPA 2.50 – 2.99

Pass – CGPA 2.00 – 2.49

**STATISTICS (HIGHER NATIONAL DIPLOMA)**

Year one

Semester one: Curriculum Table

S/No

Course Code

Course Title

L

P

Total

Prerequisite

1

STA 311

Statistical Theory III

2

3

5

2

STA 312

Applied General Statistics II

2

3

5

3

STA 313

Statistical Inference and Scientific Methods

2

3

5

4

STA 314

Operational Research I

2

3

5

5

MTH 314

Mathematical Methods II

2

3

5

6

COM 312

Database Design I

2

3

5

7

STA 315

Technical English II

1

1

2

L – Lecture

P – Practical

TH – Total Hours.

STATISTICS (HIGHER NATIONAL DIPLOMA)

Year one

Semester two: Curriculum Table

S/No

Course Code

Course Title

L

P

Total

Prerequisite

1

STA 321

Statistical Theory IV

STA 311

STA 322

Sampling Techniques II

STA 323

Design and Analysis of Experiment II

STA 324

Statistical Management and Operations

STA 325

Biometrics

MTH 322

Mathematical Methods III

MTH 314

COM 322

Database Design II

COM 312

STA 326

Research Methodology

EDP 316

Entrepreneurship

STATISTICS (HIGHER NATIONAL DIPLOMA)

Year two

Semester three: Curriculum Table

S/No

Course Code

Course Title

Total

Prerequisite

STA 411

Operations Research II

STA 314

STA 412

Sampling Techniques III

STA 322

STA 413

*Econometrics

STA 414

Economics and Social Statistics

STA 415

*Industrial Statistics

STA 416

*Medical Statistics

STA 417

Design and Analysis of Experiments III

STA 323

STA 418

Small Business Management II

STA 419

Seminar

EDP 413

Entrepreneurship Development

*Electives

**STATISTICS (HIGHER NATIONAL DIPLOMA)**

Year two

Semester four: Curriculum Table

S/No

Course Code

Course Title

Total

Prerequisite

STA 421

Operations Research III

STA 411

STA 422

Demography II

STA 423

Non-Parametric Statistics

STA 424

Statistical Computing

STA 425

Time Series Analysis

STA 426

Multivariate Method and Stochastic Processes

STA 427

Project

**STA 311: Statistical Theory III**

Distributions of the continuous type. Concept of the use of conditional distributions. Distribution of functions of random variables. Further use of the central limit theorem. Bivariate normal distribution. Concept of the Chebyshev inequality and its uses. Method of least squares estimation.

**STA 312: Applied General Statistics**

Linear relationship between two variables. Correlation between two variables. Multiple regression between two independent variables. Polynomial models of various orders. Multiple correlation analysis of two independent variable X1 and X2. Analysis of contingency tables.

**STA 313: Statistical Inference and Scientific Methods**

Scientific and natural laws. Aims and principles of statistical inference. Decision theory. Bayern’s decision theory. Other decision concepts. Logic of theories of inference, classical standard significance tests.

**STA 314: Operations Research I**

Nature of operations research. Definition and scope of linear programming. Graphical method of solving linear programming problem (involving only two variables). Simplex method of solving linear programming problems, Sensitivity analysis, Principle of duality and its application. Transportation and assignment problems Network analysis.

**STA 315: Technical English**

Writing reports “including statistical input” by using good English and appropriate layouts (formats), Professional correspondence, Reporting on a statistical investigation in an accepted format. Writing a questionnaire in good English. Short lecture on a statistical topic.

**STA 321: Statistical Theory IV**

Distributions of independent random variable. Various distributions relation to the normal Cochran’s theorem, Neyman/Pearson lemma testing of hypothesis. Methods or maximum likelihood estimation. Method of minimum variance unbiased estimation.

**STA 322: Sampling Techniques II**

Systematic sampling. Single stage cluster sampling. Stratified random sampling.

**STA 323: Design and analysis of Experiment**

Methods of increasing the accuracy of experiments. Classification of designs and analysis of variance. Randomized block design with one observation per cell. RBD with more than one observation per cell Latin square design.

**STA 324: Statistical Management and Operations**

Principles of Management. Practice and organization of Management Principles and Practice of a feasibility study.

**STA 325: Biometrics**

Basic concepts of cells in Biology. Basis for the inheritance theory. Population genetics. Basic distributions in biological models. Basic assay methods. Transformation needed in bio-medical responses. Estimations and uses of potency of substances. Other biometric distributions and their uses.

**STA 411: Operations Research II**

Basic concepts of queuing. Basic simulations techniques. Inventory theory-deterministic models only.

**STA 412: Sampling Techniques III**

Two stage sampling. Stratified two stage sampling. Radio estimate under stratified sampling. Principles regression estimation. Treatment of non-sampling error.

**STA 413: Econometrics**

Nature and quality of economic data. Measurement and functions. Application of regression and correlation to economic data. Analysis of variance, homoscedasticity and heteroscedasticity in economics. Concepts of multicolinearity. Serial and auto correlation. Errors in variance and simultaneous equation models. Lagged variables.

**STA 414: Economic and Social Statistics II**

Sources of data for economic and social investigation. Concepts of social accounting. The concepts and use of national accounting. Application of index numbers to economic and social statistics. Principles of statistical management. Application of regression and correlation in economic and social statistics.

**STA 415: Industrial Statistics II**

Concepts of statistical quality control. Process control by inspection of variables. Process control by inspection of attributes. Principles of an acceptance sampling plan. Use of statistical tests of significance in quality control.

**STA 417: Design and Analysis of Experiments III**

Gracco-Latin square design. Crossover designs. Factorial experiments. Split-plot design. Incomplete block designs.

**STA 418: Small Business Management II**

Financing of small business enterprises. Financial management in a small business enterprise. Credit control in small business enterprises. Organization and its structure for a small-scale enterprise. Small-scale enterprise information system. Marketing management of a small-scale enterprise. Small-scale enterprise information system. Marketing management of a small-scale enterprise. Business plan for a small-scale enterprise presentation on a business plan for a small-scale enterprise.

**STA 421: Operation Research III**

Revised simplex method. Definition, scope and solution of integer programming problems. Further inventory theory (non-deterministic models).

**STA 422: Demography II**

Methods of evaluating demographic data. Methods of adjusting demographic data. Basic measures of fertility. Basic measures of morality. Life tables and their construction. Reproductivity. Basic measures of migration. Population estimates and projections. Methods of estimating demographic measures from incomplete data.

**STA 423: Non-parametric Statistics**

Non-parametric testing. One sampling of test of goodness of fit. Two sample test for related samples. Two sample test of independent samples.

**STA 424: Statistical Computing **

Random numbers and methods of generating them. Numerical methods of solving equations. Solving matrix equations by numerical methods. Basic concepts of Kernel-based probability density estimation. Forming statistical algorithms.

**STA 425: Time Series Analysis**

Meaning and importance of time series analysis. Autoregressive models. Serial correclation. Application of Fourier analysis to spectral theory. Periodogram analysis. Correlogram.

**STA 426: Multivariate Methods and Stochastic Processes**

Distributions of two or more random variable. Multivariate distribution. Construction and use of discriminant analysis. Principal component analysis. Factor analysis. Hotelling’s T2 distribution. Basic concepts of stochastic processes. Markov process. Basic concepts of a poison processes. Basic concepts of birth and death processes.

**STA 427: Project**

Researching a chosen topic at HND level from available sources. Collecting data on the chosen topic. Producing a report on the chosen topic.

**COM 312: Database Design I**

Organization’s information need and database concepts. Differentiate the various types of data models, how to model data. Design of relational databases design structured query language (SQL), database system architecture.

**COM 322: Database Design II**

Object – oriented data mode and object oriented languages. Design of object-oriented databases. File structure and physical storage. (concept indexing and hashing, query processing. Concept of transactions and concurrency control. Recovery systems DBMS applications.

**MTH 314: Mathematical Methods II**

Basic concepts of series. Basic partial differentiation and its application. Basic double integration and its application. First and second order differential equations with constant coefficients.

**MTH 322: Mathematical Methods III**

Definition of a vector space and the concept of linear dependence and independence. System of simultaneous linear equation. Quadratic forms and their methods of reduction. Eigen values and vectors and their computations. First order and first degree partial differential equations and the methods of their solutions.

**ND IN STATISTICS**

**GOALS AND OBJECTIVES**

The national diploma programme in statistics is aimed at producing assistant statisticians capable of collecting data, analysing and making inference under supervision.

On the completion of this programme, the diplomate should be able to:

(i) Acquire a good knowledge of basic statistics and statistical methods.

(ii) Understand the applications of statistics in commercial, industrial and scientific environment;

(iii) Acquire a practical skill in data collection analysis and research methods;

(iv) Understand the use of computers for various purposes.

(v) Set out statistical projects under supervision.

**GOALS AND OBJECTIVES**

**ENTRY REQUIREMENT**

Applicants with any of the following qualifications may be considered for admission into the National Diploma Programme by direct entry.

(1) Five credit level passes in the West African School Certificate, Senior Secondary School Certificate, Senior Secondary School Certificate or General Certificate of Education (GCE)

Ordinary level and National Examination Council (NECO), TCII, NTC, in not more than two sitting. The subject must include mathematics and any three of the following: Statistics, Geography, Further Mathematics, chemistry, Physics, Biology, Agricultural Science, Economics. A credit pass in English Language is compulsory.

(2) Candidates who have successfully completed the Boards recognized Pre-National Diploma (Science and Technology) course. Such students must have passed Mathematics, English language and any two subject listed in (1) above.

**CURRICULUM**

The Curriculum of the ND programme consist s of four main components.

These are:

- General Studies/Education
- Foundation Courses
- Professional courses
- Supervised industrial work experience scheme (SIWES)

The General Studies/Education component shall include compulsory in English language and Communication and social Studies. Citizenship (the Nigeria Constitution).

The General Education component shall account for not more than 10% of total contact hours for the programme.

**Foundation courses** – Courses in Mathematics, Computer Studies. Descriptive geometry and basic statistics. The number of hours will vary with the programme and may account for about 10-15 of the total contact hours.

**Professional Courses** – Courses which give the student theory and practical skills he needs to practice in his field of calling at the technician/technologist level. These may account for between 60 – 70% of the contact depending on programme. Supervised Industrial Work Experience Scheme (SIWES) shall be taken during the long vacation following the end of the second semester of the first year.

**CURRICULUM STRUCTURE**

The structure of the ND Programme consist of four semesters of classroom, laboratory and workshop activities in the college and a semester (3 – 4 months) of supervised industrial work experience scheme (SIWES)

Each semester shall be of 17 weeks duration made up as follows:

15 contact weeks of teaching, i.e. lecturer recitation and practical exercises, etc, and 2 weeks for tests, quizzes, examinations and registration.

SIWES shall take place at the end of the second semester of first year.

**CONDITIONS FOR THE AWARD OF THE ND**

Institutions offer accredited programmes for the award of the National Diploma to candidates who successfully completed the programme after passing prescribed course work, examinations, diploma project and the supervised industrial work experience. Such candidates should have completed a minimum of between 90% and 100% of credit units depending on the programme. Diploma certificate shall be awarded based on the following classifications:

Distinction – CGPA 3.50 – 4.0

Upper Credit – CGPA 3.00 – 3.49

Lower Credit – CGPA 2.50 – 2.00

Pass – CGPA 2.00 – 2.49

**STATISTICS (NATIONAL DIPLOMA)**

Year One

Semester One: Curriculum Table

S/No

Course Code

Course Title

Total

Prerequisite

STA 111

STA 112

MTH 111

MTH 112

COM 101

STA 113

GNS 111

ECO 111

Descriptive Statistics I

Elementary Probability Theory

Logic and Linear Algebra

Functions and Geometry

Introduction to Computing

Technical English I

Citizenship Education I

Economics

L – Lecture

P – Practical

TH – Total Hours

STATISTICS (NATIONAL DIPLOMA)

Year One

Semester Two: Curriculum Table

S/No

Course Code

Course Title

L

P

Total

Prerequisite

STA 121

Descriptive Statistics II

STA 122

Statistical Theory I

STA 123

Demography I

MTH 121

Calculus I

COM 123

Computer Packages I

GNS 121

Citizenship Education II

EDP 126

Introduction to Entrepreneurship

STATISTICS (NATIONAL DIPLOMA)

Year Two

Semester three: Curriculum Table

S/No

Course Code

Course Title

Total

Prerequisite

STA 211

Statistical Theory II

STA 122

STA 212

Elements of Sampling Theory

COM 123

STA 213

Economics and Social Statistics I

STA 214

Industrial Statistics I

MTH 212

Calculus II

MTH 213

Linear Algebra

COM 215

Computer Packages II

EED 216

Practice of Entrepreneurship

STA 215

Seminar

STATISTICS (NATIONAL DIPLOMA)

Year Two

Semester four: Curriculum Table

S/No

Course Code

Course Title

Total

Prerequisite

STA 221

Design and Analysis of Experiment I

STA 122

STA 222

Sampling Techniques I

COM 123

STA 223

Applied General statistics I

STA 224

Biostatistics I

MTH 222

Mathematical Methods I

COM 224

Management and Information Systems

STA 225

Small Business Management I

STA 226

Project

**STA 111: Descriptive Statistics I**

Nature of statistical data, their types and uses. Procedures for collection of statistical data. Difference between total coverage and partial coverage in data collection. Methods of data compilation. Methods of data presentation.

**STA 112: Elementary Probability Theory**

Concepts of set and set operations. Mapping, function and relation. Concept of permutations and combinations as used in probability. Concept of a sample space. Basic concepts of probability.

**STA 113: Technical English 1**

Writing reports, including statistical input by using English and appropriate layouts (formats). Engaging in professional correspondence. Writing a full report on a statistical investigation in an accepted format. Construction of a poster on a statistical topic. Delivering a short lecture on a statistical topic.

**STA 121: Descriptive Statistics II**

Measures of central tendency. Measure of positional values. Measures of variability. Concepts of skewness and kurtosis.. concept of time and series. Concept of index numbers.

**STA 122: Statistical Theory I**

Concept of random variable. Discrete probability distribution. Concept of mathematical expectation. Distributions of the function of discrete random variables. Mathematical expectation.

**STA 123: Demography I**

Meaning and nature of demography. Basic demographic concepts. Basic measures of fertility. Basic measure of mortality. Life table.

**STA 211: Statistical Theory II**

Concept of continuous random variables. Concept of continuous probability distributions. Normal distribution and its applications. Concept of the expectation of continuous random variables. Moments and on moment generating function of probability distributions.

**STA 212: Elements of Sampling Theory**

Concept of Sampling, Normal, student-t, chi-square and f-distributions in sampling theory. Concept of sampling distributions for samples drawn from Normal population. Concept of the central limit theorem. Concept of estimation theory. Methods of point estimation theory. Construction of confidence intervals for means standard deviation and proportions. Concept of simple test of hypothesis.

**STA 213: Economic and Social Statistics I**

Organisation of a statistical system with emphasis in Nigeria. Nature and importance of economic and social statistics. Application or index numbers. Standardization of rates, economic time series.

**STA 214: Industrial Statistics I**

Importance of statistics in industry. Concept of process of process control. Construction of control charts. Acceptance sampling schemes.

**STA 221: Design and Analysis of Experience I**

Principles of planning, simple statistical experiments. Simple experimental designs. Role of analysis of variance in experimental design.

**STA 222: Sampling Techniques I**

Statistical Universe and Sample. Methods of sampling. Planning of a sample survey. Execution of a sample survey. Analysis of sample survey results. Errors and biases of sample surveys. Estimate population parameters under simple random sampling. Methods of regression and ratio estimation.

**STA 223: Applied General Statistics I**

Theory of linear regression. Association and correlation between two variables. Simple contingency table (m x n). Simple non-parametric test.

**STA 224: Biostatistics I**

Importance of Statistics in biology and medicine. Concept of vital and health statistics. Standardised rates. Simple genetics and bioassays.

**STA 226: Small Business Management 1**

Nature of small-scale enterprises. Legal framework for small-scale enterprises. Role of governments in small-scale enterprises in Nigeria. Business plan for a small-scale business enterprise. Marketing management in a small business enterprise. General concept of production management. Human capital needs for an enterprise.

**STA 226: Seminar**

Research a chosen topic at ND level from available sources. Collect data on the chosen topic. Produce a report on the chosen topic.

**COM 101: Introduction to Computers**

History, Classification and impact of computers. Concept of computer hardware. Concept of computer software. Computer data processing systems. Procedures for computer and data preparation method. Security and safety procedures within a computer environment. Concept of a computer network. The use of the internet.

**COM 123: Computer Packages I**

Existing application packages. Word processing packages. Electronic spread sheets. Fundamentals of accounting packages. Presentation packages. The use of education, medical and other packages.

**COM 215: Computer Packages II**

Common graphics packages. Concept of computer aided design. Database management. Date analysis package.

**COM 224: Management Information Systems**

Different systems, systems theory. Concept of management information. Features of management information systems. (MIS). Concept of transaction processing. Concept of office automation. Different applications of MIS principles of decision making Development cycle of an MIS. Principles of project management. Total systems.

**MTH III: Logic and Linear Algebra**

Concept of logic and abstract thinking. Concept of permutations and combinations. Binomial expansion of algebraic expressions. Algebraic operations of matrixes and determinants.

**MTH 112: Functions & Geometry**

Concept of function and relations. Special properties of functions. Algebra of functions. Fundamental elements of trigonometry. Analytic geometry of a straight line. Concept of symmetry and their application to comic sections.

**MTH 121: Calculus I**

Concept of limits. Concept of continuity Techniques of different differentiation. Various application of derivations. Integration as the reverse of differentiation.

**MTH 212: Calculus II**

Summations of finite double series. Meaning of convergence of infinite series. Concept of a power series. Limits.

**MTH 213: Linear Algebra**

Matrices and their algebra (Contd). Determinants (contd). Solutions of systems of linear equation using matrices and numerical methods. Basic concepts and manipulations of vectors and their application to engineering problems. Eigen values and eigen vectors.

**MTH 222: Mathematical Methods I**

Meaning of a complex numbers, Algebra of complex numbers. Nature of a differential equation. Exact differential equation. Extract differential equations of first order. Theory of linear differential equations properties and space vectors. Scalar and vector products. Applications of the concept of vectors to plane geometry.