


Politecnico di Torino  
Academic Year 2017/18  
12CKRPL, 12CKRPI Statistics 

1st degree and Bachelorlevel of the Bologna process in Engineering And Management  Torino 





Esclusioni: 10CKR 
Subject fundamentals
The use of statistical methods and probability models for analyzing data has become common practice in all business and industrial sectors. This course aims at providing a comprehensive introduction to those models and methods most likely to be encountered and used by students in their careers in engineering. Output of statistical software are examined, due to the importance of statistical software in particular for the analysis of large datasets. Problems and casestudies that frequently occur in practice are examined.

Expected learning outcomes
Decision making has to be based on pieces of appropriate and good quality information: statistical methods are vital tools in order to get, select and work out information. Therefore the learning outcome of the course is aimed to provide the students of methodologies in order to afford advanced elaborations and working knowledge of the most popular techniques among the experimenters. Practical problems that frequently occur are used as examples in order to enlighten limits and features of the proposed methods. The transferable skills is to supply statistical tools to analyze experimental data.

Prerequisites / Assumed knowledge
The complete program of the current courses of Mathematical Analysis and Geometry (including Linear Algebra) or equivalent education.

Contents
Descriptive Statistics. Population, sample and different sampling techniques; graphical representations; main indices of central tendency; variability and its indices; twodimensional characteristics and their representation.
Probability. Different definitions of probability and their use in different contests; rules for computing the probability; conditional probability, Bayes, stochastic independence. Distributions. Random variable; discrete and continuous random variables; main parameters for position, variability and shape; main theoretical distributions. Statistical Inference. Sampling distributions, central limit theorem and its applications and implications, point estimation, estimators and their properties, confidence interval and confidence limits for means, pair observations and variances. Analysis of Variance and Covariance: partitioning the variability; designed experiments and controlled factors: assigning the variability to different factors; main effects and interactions; significance test for main effects and interactions. Discussion of software outputs. Modeling. Linear regression model (exploratory data analysis, parameters estimation, check of the estimations quality, prediction). Decomposition of the variability; assigning the observed variability in designed experiments to the single variables; statistical tests for the variables significance. Discussion of software outputs. 
Delivery modes
Traditional exercise sessions will complement lectures; practical problems and casestudies that frequently occur are examined besides the rigorously theoretical lessons, using a number of examples and casestudies: Whereas appropriate statistical software will be taught in the computer laboratory.

Texts, readings, handouts and other learning resources
Lesson book: Grazia Vicario, Raffaello Levi (2014), Metodi statistici per la sperimentazione, Casa Editrice Esculapio, Bologna, will be used as the reference textbook.
Exercise book: G. Vicario, R. Fontana (2014), Laboratorio di Metodi statistici per la sperimentazione – Problemi svolti ed esercizi, Casa Editrice Esculapio, Bologna, will be used as the reference exercisebook. May be the students will be given some issues of exercises and/or Statistic Laboratory. 
Assessment and grading criteria
The exam consists of a test and an oral exam. The test consists of exercises (multiple choice) and concerns all the subjects dealt during the lessons and in the laboratories. During the exam formulary is provided, no books and other teaching material are allowed. The maximal mark is 24/30 and the minimal mark to be admitted to the oral exam is 12/30. The oral exam consists of the discussion of an output created with the software used in the laboratories and of some theoretical questions. The final mark is the mark of the test plus or minus 8 points according to the valuation of the oral exam.

