Statistics

Code:

EC0030

Acronym:

ESTA

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2013/2014 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/mod/forum/discuss.php?d=7053#p14584
Responsible unit:	Mathematics Division
Course/CS Responsible:	Master in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEC	260	Syllabus since 2006/2007	2	-	6,5	60	174

Teaching language

Portuguese

Objectives

JUSTIFICATION:
Essentially, two reasons justify the existence of this unit: the need to develop a scientifically based  reasoning, the capacity of presenting arguments and of communicating in scientific and technical approaches in different domains of civil engineering; the need for acquiring scientific knowledge of probabilistic and statistical nature for use in the subjects that will be studied in the remaining semesters of the course.

OBJECTIVES:
To induce an educational background for other following subjects in the curricula. To give solid knowledge for future developements at the specialization level as well as at the professsional level. To prepare the student for the use of probabilistic and statistical language and to be able to comunicate when dealing with subjects in which Probabilities and Statistics take part, ensuring that a correct interiorization of concepts is achieved. To educate the student to be able to translate his reasoning into mathematics when analysing real world problems and adequately formulate these problems. To educate the student in techniques that can be used in order to solve these problems. To be able to efiently use software solving problems that require techniques or envolve statistical or probabilistic concepts.

Learning outcomes and competences

RESPONSIBILITIES AND OUTCOMES OF LEARNING:
Development skills (CDIO): technical knowledge in basic sciences (ie in Statistics), personal and professional skills of thinking and problem solving engineering, experimentation and knowledge discovery, knowledge engineering and advanced skills and attitudes ; interpersonal communication skills (oral and written).
The student should be able to:
- Describe data sets by applying statistical techniques;
- Compute probabilities in complex situations, including those that use random variables of one or two dimensions, following or not typical distributions;
- Use the properties involved in the use of typical distributions;
- Solve estimation problems

- Apreend the philosophy of hypothesis testing

- Solve problems involving the goodness of fit of distributions and discuss their fitness

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The student should have knowledge of mathematics taught in previous semesters, for example, on the use of functions of one or more variables, sequences and series and numerical analysis including the use and implementation of calculations with the help of calculators and computers.

Program

Brief presentation of the statistical method in the context of Civil Engineering and uncertainty in Engineering.
Descriptive statistics: different types of statistical variables; univariate distributions (graphical representations and statistical measures); bivariate distributions (marginal and conditional distributions), dependency between statistical variables (shape, minimum square method, regression line, correlation coefficient).
Probability spaces (generalization of concepts, axioms, and properties, classical concept of probability, conditional probability, independence of events).
Unidimensional random variables: discrete and continuous; distribution functions; probability functions; probability density functions; brief reference to variable transformations; mathematical expectation; moments and order parameters.
Two-dimensional random variables: joint distribution, marginal distributions and conditional distributions; independence; mathematical expectation of vectors.
Typical distributions: discrete (uniform, Bernoulli, binomial, multinomial, hypergeometric, Poisson) and continuous (uniform, exponential, gamma, Gauss, lognormal, Qui2); properties of Gaussian law.
Approximations of distributions: Central Limit Theorem and most known approximations.
Estimation: statistics and estimators, estimators for the mean, the variance and the linear correlation coefficient; confidence intervals.
Hypothesis testing: philosophy of testing; goodness of fit testing.
Initiation to the simple linear regression models.

DISTRIBUTION:
Scientific component: 85%
Technological component: 15%

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
The thematic of this curricular unit emphasize the need to develop a scientifically based reasoning, the capacity of presenting arguments and of communicating in scientific and technical approaches in different domains of civil engineering, in particular leading to the education to deal with uncertainty in engineering; the need for acquiring scientific knowledge of probabilistic and statistical nature for use in the subjects that will be studied in the remaining semesters of the course.

Mandatory literature

Douglas C. Montgomery, George C. Runger; Estatística aplicada e probabilidade para engenheiros. ISBN: 85-216-1360-1 (English original: Montgomery, Douglas C.;Applied Statistics and Probability for Engineers. ISBN: 0-471-17027-5 )
Paula Milheiro Oliveira; Estatística - Apontamentos da cadeira, disponíveis na Editorial, FEUP
Paula Milheiro de Oliveira; Estatística - Colecção de exercícios, Feup (available in Moodle site)

Complementary Bibliography

Paulino, C.D. e Branco, J.A.; Exercícios de Probabilidade e Estatística, Escolar Ed, 2005
Moore, David S.; Introduction to the Practice of Statistics. ISBN: 0-7167-1989-4
Bento Murteira, C.S. Ribeiro, J.A. Silva. C. Pimenta; Introdução à Estatística, Escolar Editora, 2010
Pestana, Dinis Duarte; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9
Andreia Hall, Cláudia Neves, António Pereira; Grande maratona de estatística no SPSS. ISBN: 978-972-592-301-6

Teaching methods and learning activities

It is essentially a formative subject, coordinating fundamental theoretical knowledge with some approaches which are necessary in the subjects placed ahead in the curricula. At this level it is important to develop intuitive concepts as well as computational ability. The concepts are exposed in a clear and objective way, making frequent use of examples of physical or geometrical nature. The use of statistical software is encouraged, as a working tool, namely through the execution of 2 working projects in the computer room (1 hour duration each). A total of at leat 5 sessions are held in the computer rooms and the others have intensive use of calculators. Calculators are also used during part of the written exams.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The teaching methodologies allow the students be able to describe data sets by applying statistical techniques, compute probabilities in complex situations, including those that use random variables of one or two dimensions, following or not typical distributions, use the properties involved in the use of typical distributions solve estimation problems, solve problems involving the goodness of fit of distributions and discuss their fitness, learn the philosophy of hypothesis testing.

Software

SPSS 17.0
Excel

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Trabalho laboratorial	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	85,00
Total:	85,00

Eligibility for exams

Achieving final classification requires compliance with attendance at the course unit, according to the MIEC assessment rules.

Calculation formula of final grade

CP: total classification in the 2 working projects (rounded to one decimal)

CE: classification in the writing paper (rounded to one decimal)


final classification = 0,250 * CP + 0,750 * CE


NOTE 1: The distributed evaluation obtained in previous courses is not valid.

NOTE 2: The working projects are compulsory. No delivery of the working projects results in "zero" mark in the associated component.

Examinations or Special Assignments

The two working projects mentioned above (TPs) are done during laboratory classes, according to the student's schedule (see moodle).

The TPs are compulsory. Students who have their absence justified and accepted by the Degree Director will have the TP'dates altered to timetables of the other class'groupes and thus need to contact the teacher urgently, so that the new hour is set for their assessment. Only in cases for which this change is impossible the TPs will be schedulled to the 15th week of the calendar, day/time to be announced.

 

Special assessment (TE, DA, ...)

Final written exam for the Written Exam Component. For the component regarding the working projects the assessment made along the academic semester remains valid.

Knowledge of Portuguese;
Frequency introductory graduate courses in the scientific field in this discipline;
Assessment by examination and / or work (s) defined in accordance with the student profile

Classification improvement

Final written exam for the Written Exam Component. For the component regarding the working projects the assessment made along the academic semester remains valid.

Observations

In the written examination, during the first part of the test, the use of  a calculor is forbiden.