Estudia
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- Doble Grado en Ingeniería Civil e Ingeniería de los Recursos Mineros y Energéticos
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Estadística
- Tutorías Grupales (2 Hours)
- Clases Expositivas (28 Hours)
- Prácticas de Laboratorio (14 Hours)
- Prácticas de Aula/Semina (14 Hours)
Statistics is part of the basic training module (Mathematics) in the field of Engineering. The subject is instrumental and can be related to any of the fields of the degree in which experimentation is not deterministic, but similar situations give rise to different results. This tool is vital for engineers as it allows them to understand phenomena subject to variation and effectively predict, explain or sometimes control them.Scientific knowledge in Engineering is increasingly based on statistical solutions. When presenting results, it is essential to know and handle the best techniques and be aware of the scope of the conclusions. In the same way, the processes of production, product development, manufacturing, marketing, finance, human resources, purchases, sales, etc., require experimentation and quality control, for which Statistics is fundamental. In this way, an engineer who masters the different statistical techniques can become much more effective in all phases of his work, especially those that have to do with research, development and production.
The objective of the Statistics course is to introduce the main concepts of descriptive statistics, probability and inference through examples. The contents are adapted to the needs of Engineering students. Statistics will be understood as a tool to solve specific problems, so all the examples and problems proposed will reproduce realistic practical situations. One of the most important tasks will be to express these concrete problems in statistical terms. In this way the standard methods can be easily applied. The importance of presenting the statistical conclusions in their context, so that they can be understood without technical knowledge, will be emphasized.The contents refer mainly to the description, formalization and analysis of experimental data, which constitutes the core of the statistical process. Specifically, the first module will introduce the most useful descriptive sample measures of central location, dispersion, position and shape in the context considered. A second module will be dedicated to the formalization of the study of populations through the Probability Calculus. This study has a double objective. On the one hand, the most common theoretical models in engineering will be introduced, which can be used when the knowledge of the population is sufficiently broad. On the other hand, if it is difficult to get to know the entire population, Probability Calculus will be used as a tool to be able to make inferences about the populations from the samples. The inferential process will be analyzed in a third module.
Recommended prior competencies are:1. Capacity for abstraction: move from colloquial language to mathematical language (and vice versa).2. Manage and understand basic mathematical symbols.3. Manage the basic concepts of set theory and its applications.4. Handle and understand the real function with real variable.5. Operate with the usual functions in Engineering (logarithmic, exponential, potential, etc.).6. Convert units from one scale to another.Recommended prior knowledge is:1. It is very convenient that you have completed the subject of Mathematics II or Mathematics applied to Social Sciences in the 2nd year of Baccalaureate.2. It is recommended to have completed all the subjects of Mathematics of the Baccalaureate.3. It would also be desirable for the student to have taken the subjects of "Linear Algebra" and "Calculus" in the 1st semester of this degree.
At the end of the semester, students are expected to acquire the following general skills indicated in the degree verification report:
CG02 Understanding of the multiple conditions of a technical and legal nature that arise in the construction of a public work, and the ability to use proven methods and accredited technologies, in order to achieve the greatest efficiency in construction while respecting the environment and the protection of the safety and health of workers and users of public works.
Statistics is part of the basic training module, helping to acquire the following specific competence:
CB01 Ability to solve mathematical problems that may arise in Engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial derivative equations; numerical methods; numerical algorithmic; statistics and optimization.
These competencies can be specified in that the student must be able to achieve the following learning outcomes:
M1RA11 Collect data, present it in a clear and summarized way, and analyze the results.
M1RA12 Make forecasts for different working conditions and estimate their reliability.
M1RA13 Use statistical models in solving real problems.
M1RA14 Make decisions in an environment of uncertainty.
In the same way, the learning outcomes are specified in the student being able to:
1. Distinguish the different stages involved in the statistical process (from data collection to writing the technical report with the fundamental conclusions) that are necessary to carry out a correct and transparent study.2. Manage the different measurement scales and their possibilities in statistical analysis.3. Discriminate between the objectives of a statistical analysis: descriptive and inferential.4. Distinguish between a statistical population and a sample of it.5. Understand the information provided by a statistical table that orders the data of a sample.6. Organize, filter, describe and synthesize experimental data. Summarize the information of a sample through measures of centralization, dispersion and position.7. Compare the information obtained from different samples.8. Recognize the degree of dependence between different characteristics of a sample.9. Using a function (linear or non-linear) to model the dependence between the different characteristics of the sample. Use the model for prediction. Reliability of it.10. Know the probabilistic basis of statistical inference.11. Assign statistical models to different behaviors in real life. Identify the different distributions.12. Use descriptive techniques of classification and obtaining information through characteristic parameters of the sample or population analyzed.13. Recognize the different sources of error that can arise in the design of experiments and data analysis in order to control and report their effect.14. Estimate unknown parameters of a population from a sample.15. Manage principles and applications of statistical hypothesis tests.16. Compare two populations based on their characteristic and unknown parameters.17. Formulate real problems in statistical terms (estimation of parameters, contrast of hypotheses,...) and apply Statistical Inference to their resolution and make decisions based on experimental data.18. Judge the correctness of published statistics, locating the critical points where appropriate.19. Possess skill in handling tables, calculators and statistical packages.20. Being able to use Statistics as a necessary tool in their future professional practice.
DESCRIPTIVE STATISTICS: Basic concepts: Population and sample. Parameters and statistics. Frequency distributions. graphic representations. Measures of central tendency, position and dispersion. Linear regression and correlation. Other types of regressionPROBABILITY CALCULUS: Events. Concept of probability and properties. Fundamental theorems in probability: Bayes' theorem. Random variable. Distribution function. Most common probability models in Engineering, their most important characteristics and their applications.STATISTICAL INFERENCE: Point estimate. Interval estimation: confidence coefficient. Construction of confidence intervals for the usual parameters. Parametric hypothesis testing: Concepts related to hypothesis testing. Non-parametric tests, normality tests. Inference in regression.PRACTICES: Practice 1. Introduction to R and R Commander (2 hours) Practice 2. Preparation of the data set. Frequency table (2 hours) Practice 3. Graphic and exploratory analysis. (2 hours) Practice 4. Numerical summary. Comparison of distributions. (2 hours) Practice 5. Descriptive Regression. (2 hours) Practice 6. Statistical Inference. (2 hours) Practice 7. Statistical Inference: regression. (2 hours)
1.- Group learning with the teacher.A combination of lecture, problem-based learning and basic practical examples will be used in the lectures. In this way, the teacher will be able to focus on the most important ideas of each subject, discriminating what is fundamental from what is most accessory, and present a certain way of working and studying the subject.In classroom practices, if the number of students is around 40, the participatory model and teamwork will be used as an essential element in problem-based learning. The teacher will encourage communication with the students. A similar methodology will be used in laboratory practice classes, as well as in group tutorials. In laboratory practices, student participation in experimentation will be favored, with the approach of real and simulated examples. Students must prepare the material prior to classes so that conceptual doubts can be discussed during contact hours and they must dedicate the necessary time to solving guided exercises.2.- The individual study.The personal work that a student must do to acquire the capacity for abstraction that allows him to apply statistical procedures to the various problems that he will be facing is important. It will try to direct the student in activities oriented to problem-based learning using a wide range of realistic situations that an engineer can face with the help of Statistics.3.- Student group work.In the classes of classroom practices, laboratory practices and group tutorials, students will be encouraged to work in groups. Communication will be promoted, indicating the advantages of solidarity in the search for common goals and the sharing of responsibilities.4.- Tutoring.The tutorials are carried out individually to resolve those doubts that the student has not solved on their own. The student will also be given the possibility of raising their doubts through email. In the group tutorial classes, some of the more general problems that the student encounters in order to acquire the skills can be discussed.
The hours dedicated to the different parts of the subject, and which are listed in the table above, must be considered approximate.
FACE-TO-FACE WORK | NON FACE-TO-FACE WORK | |||||||||||
Units | Total hours | Theoretical lessons | Classroom practices / Seminars / Workshops | Laboratory practices / field / computer room / language classroom | Hospital clinical practices | Group tutorials | External Practices | Evaluation Sessions | Total | Group work | Autonomous work | Total |
DESCRIPTIVE STATISTICS | Aprox. 37 | 5 | 4 | 4 | 1 | 14 | 23 | |||||
PROBABILITY CALCULUS | Aprox. 55,25 | 14 | 5 | 0 | 1 | 1,5 | 21,5 | 33,75 | ||||
STATISTICAL INFERENCE | Aprox. 57,75 | 7 | 4 | 9 | 1 | 1,5 | 22,5 | 35,25 | ||||
Total | Aprox. 150 | 26 | 13 | 13 | 2 | 4 | 58 | 92 |
The hours dedicated to the different parts of the subject, and which are listed in the table above, must be considered approximate. Exceptionally, if health conditions require it, non-face-to-face teaching activities may be included. In which case, the student body will be informed of the changes made.
MODALITIES | Hours | % | Totals | |
Face-to-face work | Theoretical lessons | 26 | 44.83% | 58 (38.67%) |
Classroom practices / Seminars / Workshops | 13 | 22.41% | ||
Laboratory practices / field / computer room / language classroom | 13 | 22.41% | ||
Hospital clinical practices | ||||
Group tutorials | 2 | 3.45% | ||
External practices | ||||
Evaluation sessions | 4 | 6.90% | ||
Non face-to-face work | Group work | 92 (61.33%) | ||
Autonomous work | ||||
Total | 150 |
The evaluation of the subject consists of two parts. In both, it will be assessed whether the student acquired the skills and learning outcomes expected at the beginning of the semester.The first part consists of assessing whether the student acquired the skills set out at the beginning of the semester, taking into account the autonomous and group work carried out in class. In this first part, the autonomous or group work carried out by the student during the course will also be assessed, as well as their active participation in the development of the subject. The total weight of this part is 40% in the final grade. This first part corresponds to the "continuous evaluation" of the subject and as such will be evaluated only once in the terms described below, keeping the grade obtained for both the corresponding Ordinary and Extraordinary calls. The evaluation of this first part of the subject (continuous evaluation) is detailed below: tests related to the practical classes will be carried out to find out if the student achieved the expected learning results (RES 1 to RES 8) through the use of the statistical package R that will have handled previously with a weight of 30% in the final grade. The tests, agreed by all the practice teachers, will consist of solving exercises and executing real and/or simulated tasks according to the resolution methodology used throughout the subject with the help of the statistical package R to perform the necessary calculations. in each case. There will also be exercises that the student will solve in class on a date to be specified related to the probability calculation module with a total weight of 10% in the final grade. Students who have actively participated continuously throughout the course may receive an additional 2%. It should be noted that if the student had not attended any of the evaluations described, their grade will be 0 points.
The second part consists of verifying if the student reached the foreseen capacities by means of the evaluation of the learning results achieved. To do this, a theoretical-practical exam will be held at the end of the semester. This exam also scores a part of the student's autonomous and group work, corresponding to concepts knowledge, problem solving and the ability to communicate and transmit them in written form (in this case linguistic and spelling errors may be penalized). The test will consist of the resolution of theoretical/practical exercises and execution of real and/or simulated tasks according to the resolution methodology used throughout the course. The total weight of the same in the final grade is 60% (all the material of the subject - including that explained in the practical classes - is evaluated in this exam). The evaluation of this part may be carried out through objective type questions (multiple choice) or non-objective (developing or short answer), or both types.Differentiated assessment students will only take the final exam (which will represent 100% of their grade) in which, as mentioned above, all the subject matter is assessed.In the extraordinary calls, an exam will be carried out equal to that of the second part of the subject, keeping the score obtained in the continuous evaluation (those who have not taken the continuous evaluation will have a 0 in said part).
Exceptionally, if health conditions require it, remote evaluation methods may be included. In which case, the student body will be informed of the changes made.
Assessment systems | Learning outcomes | Percentage |
Exam on laboratory practices (with execution of real and/or simulated tasks) and evaluation of individual and group work and active participation in class. | CB1, CG3, CG4, CG5, CG14, CG15 (from RES 1 to RES 8) | 30 + 2 additional if applicable |
Exercises solved in class on specific dates (Probability Calculus Module) | CB1, CG3, CG4, CG5 (from RES 1 to RES 8) | 10 |
Theoretical-practical exam (written test and execution of real and/or simulated tasks) | CB1, CG3, CG4, CG5 (from RES 1 to RES 8) | 60 |
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