Statistics and Data Analysis
A.Y. 2026/2027
Learning objectives
The course aim at introducing the fundamentals of descriptive statistics, probability and parametric inferential statistics.
Expected learning outcomes
Students will be able to carry out basic explorative analyses and inferences on datasets, they will know the main probability distributions and will be able to understand statistical analyses conducted by others; moreover, they will know simple methods for the problem of binary classification, and will be able to evaluate their performances. The students will also acquire the fundamental competences for studying more sophisticated techniques for data analysis and data modeling.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Introduction to python.
Descriptive statistics:
- Frequencies and cumulate frequencies. Joined and marginal frequencies.
- Indices of centrality, dispersion, correlation, heterogeneity, and concentration.
- Graphical methods: frequency and cumulative frequency plots, scatter plots, and QQ plots.
- Classificators and ROC curves.
Probability:
- Combinatorics. Basics of set theory.
- Probability axioms.
- Conditional probability and related theorems.
- Discrete and continuous random variables. Centrality and dispersion indices for random variables and their properties.
- Multivariate random variables. Covariance and correlation indices for random variables.
- Independent events and independent random variables.
- Markov and Tchebyshev inequalities.
- Bernoulli, binomial, geometric, Poisson, discrete uniform and hypergeometric models.
- Continuous uniform, exponential and gaussian models.
- Poisson process.
Parametric inferential statistics:
- Population, random sample and point estimates.
- Sample mean. Central limit theorem.
- Sample variance.
- Unbiasedness and Consistency in mean square.
- Methods for estimation determination.
- Large numbers law.
- Computation of the sample size.
Descriptive statistics:
- Frequencies and cumulate frequencies. Joined and marginal frequencies.
- Indices of centrality, dispersion, correlation, heterogeneity, and concentration.
- Graphical methods: frequency and cumulative frequency plots, scatter plots, and QQ plots.
- Classificators and ROC curves.
Probability:
- Combinatorics. Basics of set theory.
- Probability axioms.
- Conditional probability and related theorems.
- Discrete and continuous random variables. Centrality and dispersion indices for random variables and their properties.
- Multivariate random variables. Covariance and correlation indices for random variables.
- Independent events and independent random variables.
- Markov and Tchebyshev inequalities.
- Bernoulli, binomial, geometric, Poisson, discrete uniform and hypergeometric models.
- Continuous uniform, exponential and gaussian models.
- Poisson process.
Parametric inferential statistics:
- Population, random sample and point estimates.
- Sample mean. Central limit theorem.
- Sample variance.
- Unbiasedness and Consistency in mean square.
- Methods for estimation determination.
- Large numbers law.
- Computation of the sample size.
Prerequisites for admission
Students shall have passed the exam of "Matematica del continuo" (calculus); besides that, the course requires knowledge of the main topics of computer programming, and having passed the exam of "Matematica del discreto" (discrete mathematics) is strongly suggested.
Teaching methods
Frontal classes and exercise sessions. Lecture attendance is strongly advised.
Teaching Resources
Suggested textbooks:
- S. Ross, Introductory statistics, Academic Press, 2010, ISBN 9788838786020
- S. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 5th edition, Academic Press, 2014, ISBN 9780123743886
Lecture notes (for topics not covered in the suggested textbooks) and sample code available at the course Web pages:
- https://labonline.ctu.unimi.it/
- https://malchiodi.di.unimi.it/teaching/SAD/
- S. Ross, Introductory statistics, Academic Press, 2010, ISBN 9788838786020
- S. Ross, Introduction to Probability and Statistics for Engineers and Scientists, 5th edition, Academic Press, 2014, ISBN 9780123743886
Lecture notes (for topics not covered in the suggested textbooks) and sample code available at the course Web pages:
- https://labonline.ctu.unimi.it/
- https://malchiodi.di.unimi.it/teaching/SAD/
Assessment methods and Criteria
The assessment consists of a compulsory written examination, lasting two and a half hours, and an oral examination.
The written examination consists of open-ended questions of either a theoretical or an applied nature, with content and difficulty levels consistent with the topics covered during the course. During the examination, students may consult a formula sheet and statistical tables provided by the instructor, and may use non-programmable calculators. The consultation of any other materials, including textbooks, personal notes, or electronic devices such as mobile phones, is strictly prohibited.
The written examination is graded on a 30-point scale, and the results are communicated by email. Assessment is based on the student's level of mastery of the course material and on the correct use of mathematical notation and formalism. Passing the written examination is a necessary condition for passing the course assessment; failure to pass the written examination therefore results in failure of the examination as a whole.
The oral examination is compulsory for students who obtain a grade below 22/30 or above 26/30 in the written examination. It consists of a discussion of the student's written work and of questions concerning topics covered in the course.
The oral examination is assessed on the basis of the student's mastery of the course material, clarity of presentation, appropriateness of language, and correct use of technical terminology. The final grade for the examination, expressed on a 30-point scale, is determined on the basis of the outcomes of both the written and the oral examinations.
The written examination consists of open-ended questions of either a theoretical or an applied nature, with content and difficulty levels consistent with the topics covered during the course. During the examination, students may consult a formula sheet and statistical tables provided by the instructor, and may use non-programmable calculators. The consultation of any other materials, including textbooks, personal notes, or electronic devices such as mobile phones, is strictly prohibited.
The written examination is graded on a 30-point scale, and the results are communicated by email. Assessment is based on the student's level of mastery of the course material and on the correct use of mathematical notation and formalism. Passing the written examination is a necessary condition for passing the course assessment; failure to pass the written examination therefore results in failure of the examination as a whole.
The oral examination is compulsory for students who obtain a grade below 22/30 or above 26/30 in the written examination. It consists of a discussion of the student's written work and of questions concerning topics covered in the course.
The oral examination is assessed on the basis of the student's mastery of the course material, clarity of presentation, appropriateness of language, and correct use of technical terminology. The final grade for the examination, expressed on a 30-point scale, is determined on the basis of the outcomes of both the written and the oral examinations.
INF/01 - INFORMATICS - University credits: 6
Exercises: 36 hours
Lessons: 24 hours
Lessons: 24 hours
Professor:
Malchiodi Dario
Professor(s)