Academic management

Statistics is placed within the Module on Basic Training for Engineering, inside the subject of Mathematics, and it is taught in the second semester of the first academic year . It is an instrumental subject which can be related to any framework with non-deterministic experimentation, that is, where similar situations may give rise to different results. It is an essential topic for engineers because it allows them to understand phenomena which are subject to uncertainty and to predict them or control them in an efficient manner.

The impact of the relatively recent development of Statistics has been specially acute within Engineering. Companies usually have departments devoted to product development, marketing, finances, human resources, design or reliability, and in all of them there are problems which are solved by means of Statistics.

Statistics plays an essential role in the quality improvement of any product, which in turn contributes to increase productivity. This is a very commonly used concept which constitutes one of the main weak points of our economy. An engineer that masters the different statistical techniques may become much more effective in other areas of his work, especially in those related to investigation, development and production.  

In the course ‘Statistics’ we expect the student to acquire the ability to solve the different statistical problems that may arise in an engineering context. This means specifically the ability  to order, present and summarize data, using concepts from Descriptive Statistics; to model real-life problems by means of probabilistic models (Probability Theory); and, finally, of inferring properties from a population by means of a sample (Statistical Inference). It is also very important, in order to be able to model real-life problems, to have an adequate command of written and oral language.

The recommended previous competences are:

• Ability to move from colloquial to mathematical language, and viceversa.

• Use and understanding of basic mathematical symbols.

• Understand and use real-valued functions.

• Ability to perform elementary applications of the concept of derivative, and of the concept of integral in one variable.

• Basic knowledge of the applications of the concept of limit of a function.

• Ability to solve linear equation systems.

• Ability to solve second grade equations.

• Use of the logarithmic function.

• Ability to make transformations between different measurement scales.

The recommended previous knowledge are:

• The contents of the subject Matemáticas II or Matemáticas aplicadas a las Ciencias Sociales from the last year of high school studies.

• Those of the courses in Mathematics within the High School Studies.

At the end of the course, the students should have acquired the following general competences:

Upon passing the course, the student should have attained the following learning results:

These learning results mean that the student should be capable of:

1.    Handle the different measure scales and know their potential use within a statistical analysis.

2.    Distinguish between the two basic objectives of a statistical analysis: descriptive and inferential.

3.    Make the difference between population and sample.

4.    Understand the information provided by a statistical table that orders the elements of a sample.

5.    Summarize the information given by a simple by means of measures of central tendency, position and variation.

6.    Compare the information derived from two different samples.

7.    Know the existing connections between the different characteristics of a sample.

8.    Model by means of a function the relationship between the different characteristics of a simple, use the corresponding model to make predictions and to analyze the reliability of these.

9.    Know the probabilistic basis of Statistical Inference.

10.  Assign a probabilistic model to several real-life variables, and to identify the underlying distribution.

11.  Use classification and information retrieval techniques based on parameters from the population or the sample.

12.  Estimate unknown parameters from the population by means of a sample.

13.  Use the principles and applications of hypothesis testing.

14.  Compare two populations on the basis of some unknown characteristic parameters.

15.  Formulate real-life problems in statistical terms (parameter estimation, hypothesis testing,…), and to solve them using Statistical Inference.

16.  Be skilled in the handling of tables, calculators and statistical packages.

17.  Employ Statistics and a basic tool in his future professional career.

·         DESCRIPTIVE STATISTICS: Basic concepts: population and sample. Parameters and statistics. Frequency distributions. Graphical representations. Measures of central tendency, position and variation. Linear and non-linear regression.

·         PROBABILITY THEORY: Events. Concept of probability and basic properties. Fundamental theorems of probability: Bayes theorem. Random variable. Distribution function. Probability models in engineering: main properties and applications.

·         STATISTICAL INFERENCE: Point estimation. Interval estimation: confidence level. Confidence intervals for main parameters of interest. Parametric hypothesis testing: main concepts. Non-parametric hypothesis testing: chi-squared, goodness-of-fit, independence and homogeneity. Normality tests. Inference in regression.

The content distribution of the computer sessions is the following:

Session 1: Descriptive Statistics.

Session 2: Probability Models.

Session 3: One sample tests.

Session 4: Two sample tests.

Session 5: Independence and linear correlation.

Session 6: Linear regression.

1.- In class work.

We shall employ the model of master lesson in our theoretical classes, because it provides the lecturer with the possibility of focusing on the most important ideas in each topic, distinguishing the incidental from the essential, and presenting a particular manner of studying the subject. The classes shall include examples that help the students to understand the main applications of the subject.

In the problem solving classes we shall try to promote the participation of the students, as well as the team work. We expect that they will increase the communication level of the students among them and with the professor. A similar methodology shall be used in the experimental sessions in the laboratory and in the group tutorial sessions.

The student shall have to go through the material prior to the classes so that he can ask in these the different questions that shall arise, in order to optimize the learning process. The lecturer shall also put stress on the elements where the students usually have greater difficulties.  

2.- Individual work.

We shall try to direct the student in a number of learning-oriented activities. We shall use a research-based model, so that the student’s activity focuses in the search, analysis, manipulation, preparation and return of the information.

3.- Group work.

In the problem solving sessions, experimental sessions in the laboratory and the group tutoring sessions, we will promote the team work by the students and the development of the  communication between them, so that they share the knowledge they have acquired individually. This will also make them learn to share their responsibilities.

4.- Tutoring sessions.

Tutoring sessions shall be run individually to help the student answer the questions he has not been able to solve by himself. We shall also give the student the possibility to ask his questions by electronic mail. In the group tutoring sessions we shall discuss the main problems found by the students in the acquisition of the competences.  

The approximate number of hours that the student shall devote to the subject, both in and out of class, is given by the following table:  

Exceptionally, if the sanitary conditions require it, some online teaching activities may be put in place. In that case, the students will be informed of the changes carried out.

The student evaluation is made of three parts. In each of them we shall evaluate if the student has acquired the competences and learning results envisaged at the beginning of the semester.

In the first part we shall evaluate whether the student has acquired the competences listed at the beginning of the semester taking into account his individual work and the team work done within the classes. For this, we shall make at least one test in the laboratory sessions to determine if the student has achieved the expected learning results (RES 1 to RES 4) by means of a statistical package he has previously used. The total weight of this part is 20% of the final mark. Secondly, it shall also be evaluated the individual or team work made by the student during the course, as well as his active participation in the class. This part shall have a weight of 10% in the final mark.

The third part consists in an exam that shall take place at the end of the semester. In this exam we shall evaluate the knowledge of the different concepts, the ability to solve problems, and the ability to communicate the results in written form. It may consist of multiple choice questions, long questions, or both. The total weight of this part is 70% of the final mark.

In summary, the first sitting will consist of a written exam with a weight of 70% of the final mark, a computer exam with a weight of 20% and an evaluation of the work during the course, with a weight of 10%.

In the resits, the evaluation will be made in the following manner:

-June resit: there will be a written exam with a weight of 70%, and, on a date that shall be fixed together with the faculty, and computer exam with a weight of 20%. The remaining 10% of the mark will correspond to the one obtained during the semester. The student who attends each of the exams in this resit will give up on the mark obtained during the first resit.

-January resit: on the same date there will be a written exam coth a weight of 80% in the final mark and a computer exam with a weight of 20% in the final mark.

For those students who have certified their right to the differentiated assessment, the procedure shall be the following: a written exam with a weight of 80% in the final mark and a computer exam with a weight of 20% in the final mark.

Exceptionally, if the sanitary conditions require it, some online evaluation methods may be implemented. In that case, the students will be informed of the changes put into effect.

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M. Kendall, A. Stuart, J. Ord: ‘The advanced theory of statistics’. Charles Griffin, 1977.

M. Loève, ‘Probability theory’. Springer, 1977.

A. Papoulis, ‘Probability, random variables and stochastic processes’. McGraw Hill, 1991.

C.R. Rao, ‘Linear statistical inference and its applications’. Wiley and Sons, 1973.

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