ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 2 Expository Class: 28 Interactive Classroom: 28 Total: 58
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call:
Teaching: Sin Docencia (No Implantada)
Enrolment: No Matriculable
Introduce students to the tools of exploratory data analysis and probability theory. Provide an introduction to the open-source software R for performing descriptive analyses and generating probabilistic models.
Descriptive statistics for one variable (5 lecture hours).
Introduction to descriptive statistics. Types of data and variables.
Frequencies. Measures of location, dispersion and shape.
Graphic tools of descriptive analysis of one variable.
Two-dimensional descriptive statistics (4 lecture hours).
Joint distribution of frequencies. Tables. Marginal and conditional frequencies.
Graphic tools for two variables.
Linear dependence. Regression lines. Covariance and correlation.
Probability Calculus (7 lecture hours).
Probability space. Events. Probability. Properties.
Conditional probability. Independence. Law of total probability. Bayes' theorem.
Combinatorics
One-dimensional random variables (5 lecture hours).
Random variable. Distribution function. Types of random variables: Discrete and continuous. Mass probability function and density function.
Characteristics of a random variable. Transformation of random variables.
Main models of probability (7 lecture hours).
Discrete: Uniform, Bernoulli, Binomial, Poisson, Hipergeometric, Geometric, Negative Binomial.
Continuous: Uniform, Normal, Exponential, Gamma, Beta.
Relations of interest between the distributions.
Contents of the laboratory classes (14 laboratory hours).
The statistica package R.
Exploratory data analysis.
Generation of probability models with R.
Basic bibliography
- FREEDMAN, D. et al. (2011). Statistics. Fourth edition. Viva Books. (2º edición traducida al castellano: Estadística. Antoni Bosch, 1993).
- PEÑA, D. (2008). Fundamentos de Estadística. Segunda edición. Ciencias Sociales Alianza Editorial.
- TIJMS, H. C. (2012). Understanding Probability. Third edition. Cambridge University Press. (Dispoñible en liña a través da Biblioteca Universitaria: https://iacobus.usc.gal/permalink/34CISUG_USC/o7pcup/alma99101352186620…)
Complementary bibliography
- CAO, R. et al. (2006). Introducción a la Estadística y sus aplicaciones. Ciencia y técnica (Pirámide).
- GONICK, L., SMITH, W. (2001). Á Estadística ¡en caricaturas!. Publicado pola SGAPEIO.
- GRINSTEAD, C. M., SNELL, J. L. (1997). Introduction to Probability. Second edition. AMS.
- ROHATGI, V. K., EHSANES SALEH, A. K. Md. (2015) An Introduction to Probability and Statistics. Wiley Online Library. (Dispoñible en liña a través da Biblioteca Universitaria: https://iacobus.usc.gal/permalink/34CISUG_USC/o7pcup/alma99101352177200…).
- VERZANI, J. (2014). Using R for Introductory Statistics. 2nd Edition. Chapman and Hall. (Dispoñible en liña a través da Biblioteca Universitaria: https://iacobus.usc.gal/permalink/34CISUG_USC/o7pcup/alma99101336640220…).
According to the degree program documentation for the Mathematics degree at USC, this subject has the following learning outcomes:
Knowledge: Con01, Con02, Con03, Con04, Con05.
Skills/Abilities: H/D01, H/D02, H/D03, H/D04, H/D05, H/D06, H/D07, H/D08, H/D09.
Competencies: Comp01, Comp02, Comp03, Comp04.
In the lecture sessions, the teaching staff will present the fundamental theoretical contents of the subject, which may be complemented with the guided resolution of exercises or practical examples. The following knowledge, skills, and competencies will be addressed in these sessions: Con01; Con02; Con03; Con04; Con05; H/D02; H/D04; H/D06; H/D07; H/D08.
In the seminar sessions, active student participation will be encouraged through the autonomous resolution of proposed exercises and problems. The following knowledge, skills, and competencies will be addressed in these sessions: Con01; Con02; Con03; Con04; Con05; H/D01; H/D02; H/D03; H/D04; H/D05; H/D06; H/D07; H/D08; Comp02; Comp03.
The laboratory sessions aim to develop practical skills and illustrate theoretical concepts through applied computer-based activities. The following knowledge, skills, and competencies will be addressed in these sessions: Con01; Con04; Con05; H/D01; H/D02; H/D03; H/D04; H/D05; H/D08; H/D09; Comp01; Comp02; Comp03; Comp04.
All student activities will be supervised and guided by the teaching staff through tutorials, which may be conducted either face-to-face or online via platforms such as MS Teams.
In addition to face-to-face teaching, students will have access to the course through the University's Virtual Campus, where they will find support materials, additional resources, exercise booklets, and asynchronous communication tools.
The final grade for the subject (CA) will be the higher of the final exam grade (AF) or the weighted combination of the final exam grade and the continuous assessment grade (AC), with a relative weight of 70% and 30%, respectively:
CA = max{AF, 0.7 × AF + 0.3 × AC}
The continuous assessment (AC) will consist of two written in-person tests, which will include theoretical and practical questions, as well as exercises or problems related to the course content. These tests will take place during the course in the seminar sessions and may be conducted with the support of available class materials. The dates will be announced in advance. The number of continuous assessment tests will be the same across all interactive teaching groups, and the format will be similar. The AC grade will be calculated as the average of the two test scores. If any test is not taken, it will be scored as zero for the purpose of averaging.
The final assessment (AF) will be structured into three parts:
- Written resolution of practical questions (40%).
- Resolution of problems/exercises (40%).
- Laboratory practicals (20%).
The first two parts will be conducted during the official final in-person exam, which will be the same for all lecture groups. The part corresponding to laboratory practices will be conducted on a date established by the Faculty. The final exam grade will be the sum of the three components.
In the second exam opportunity, the same evaluation system will apply. The continuous assessment grade (AC) will be retained for both evaluation opportunities. As for the final assessment (AF), the exam grade from the first attempt will be replaced by the grade obtained in the second attempt, for both the practical questions and the problems/exercises parts. The laboratory practicals grade from the first attempt will initially be retained. However, the final exam of the second opportunity will include a specific question allowing students to improve their lab grade, in which case the highest of the two grades (from the first attempt or the specific question in the second exam) will be used.
Students who do not attend any part of the final assessment will be considered as "Not Presented."
The evaluation system for repeating students will be the same as for first-time enrollees. No grades from previous academic years will be retained.
Assessment of Learning Outcomes
Continuous Assessment (AC): Con01; Con02; Con03; Con04; Con05; H/D01; H/D02; H/D03; H/D04; H/D06; H/D07; H/D08; Comp01; Comp02; Comp03.
Final Assessment (AF): Con01; Con02; Con03; Con04; Con05; H/D01; H/D02; H/D03; H/D04; H/D06; H/D07; H/D08; H/D09; Comp01; Comp02; Comp03; Comp04.
Study and personal work time students must dedicate to pass the course
The total student workload is 25 x 6 = 150 hours. The breakdown is detailed below:
IN-CLASS WORK
Lecture hours: 28
Interactive seminar hours: 14
Interactive laboratory hours: 14
Small group tutorial hours: 2
Total in-class work hours: 58
STUDENT PERSONAL WORK
Individual or group autonomous study: 70
Preparation for continuous assessment tests: 7
Programming and other computer/lab work: 15
Total student personal work hours: 92
Attendance to classes and active participation in the proposed activities are strongly recommended as essential means for making the most of the course.
To successfully complete the course, it is advisable to attend both lecture and interactive sessions, with daily follow-up of the work done in class being fundamental.
It is also recommended that students practice using the statistical software R to explore the possibilities of the various techniques covered throughout the course.
The software used in the computer/laboratory sessions can be downloaded free of charge from the following website: http://www.r-project.org/.
Important notice: In cases of fraudulent completion of exercises or exams (plagiarism or misuse of technologies), the regulations established in the Academic Performance Evaluation and Grade Review Policy will apply.
Manuel Febrero Bande
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813187
- manuel.febrero [at] usc.es
- Category
- Professor: University Professor
Beatriz Pateiro Lopez
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813185
- Category
- Professor: University Lecturer
Alberto Rodriguez Casal
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- alberto.rodriguez.casal [at] usc.es
- Category
- Professor: University Professor
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_02 | Galician | Classroom 03 |
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 02 |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLIL_02 | Spanish | Computer room 3 |
| 12:00-13:00 | Grupo /CLIL_03 | Spanish | Computer room 4 |
| 13:00-14:00 | Grupo /CLIL_01 | Spanish | Computer room 3 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLIS_03 | Galician | Classroom 07 |
| 10:00-11:00 | Grupo /CLIS_04 | Galician | Classroom 07 |
| 11:00-12:00 | Grupo /CLE_02 | Galician | Classroom 03 |
| 13:00-14:00 | Grupo /CLE_01 | Spanish | Classroom 03 |
| Thursday | |||
| 12:00-13:00 | Grupo /CLIS_02 | Spanish | Classroom 07 |
| 13:00-14:00 | Grupo /CLIS_01 | Spanish | Classroom 07 |
| Friday | |||
| 11:00-12:00 | Grupo /CLIL_04 | Galician | Computer room 2 |
| 12:00-13:00 | Grupo /CLIL_05 | Galician | Computer room 3 |
| 13:00-14:00 | Grupo /CLIL_06 | Galician | Computer room 2 |
| 12.18.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 06.17.2026 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |