The main aim is to endow students with basic statistical tools for collecting and analysing univariate and bivariate data for political, economic and social sciences applications. Descriptive statistics provide methods for data explorative analysis. Probability theory provides models for phenomena which are subject to uncertainty. Statistical inference provides methods for analysing data obtained from random experiments. Practical lessons dealing with real-world examples are designed to allow students to improve abilities in collecting, analysing, interpreting and presenting findings and data also using statistical software and advanced spreadsheet (EXCEL). The EU digital competences DIGCOMP 2.1 are developed (Competence area 1: information and data literacy; Competence area 2: communication and collaboration; Competence area 3: digital content creation).

Knowledge and understanding: knowledge of data types and related univariate analysis techniques (frequency distributions, graphical representations, central tendency and dispersion measures), Probability theory, Statistical inference, association in two way tables, linear regression. Applying knowledge and understanding: ability to select appropriate data analysis methods analyze the relationship between variables in economics, finance and business Making judgments: ability to collect, use and critically interpret quantitative and qualitative data relating to economics and social sciences, achieved through the analysis of documents issued by official national and international statistics, scientific articles on statistical methods and applications, case studies. Digital competences are developed. Communication skills: effective communication skills of data analysis works - achieved through written tests and the presentation of research results on empirical data. Learning skills: ability to learn autonomously data analysis techniques, in professional activities or subsequent studies, achieved through the analysis of statistical methods applied in economics and social sciences

Theoretical lessons: Statistical variables. Frequency distributions. Data Graphical representations. Measures of position. Variability. Random experiment and events. Probability axioms and theorems. Conditional probability. Independence. Univariate and bivariate random variables, discrete and continue random variables. Probability distributions. Central limit theorem. Introduction to random sampling. Point Estimation. Interval Estimation. Statistical hypothesis testing. Correlation. Practical lessons dealing with real-world examples in social sciences

Cicchitelli, P. D'Urso, M. Minozzo Titolo: "Statistics: Principles and Methods" with MyLab – Pearson Seeing Theory: https://seeing-theory.brown.edu

Lectures, exercises, applied exercises, interactive visualization, case studies in social sciences based on real data, also using statistical and econometric packages and advanced spreadsheet

The final examination consists of a written test and a Project Work on real data. The written exam consists of two papers with evaluation out of thirty. The first test takes place during the midterm week (19 to 24 october, 2026); the second test takes place during the first exam session. The final score is the sum of the scores of the two tests. The first test and the second test are graded in fifteenths. During the first session, it is possible to keep the first test valid and take only the second test (note that the student can take it only once; in case of withdrawal, the test is not counted). If the student fails the midterm, he/she may take the full midterm with an assessment out of thirty. The evaluation of the midterm test may not be accepted; in that case the student may take the full test during the examination session. For tests taken during the examination session, the student is allowed to withdraw for the duration of the test, while in the case of handing in the paper, the grade obtained may not be rejected by the student in any way. The written test consists of theoretical and empirical questions, including multiple choice. It tests the acquisition of Knowledge and Understanding, Application of Knowledge and Understanding, Autonomy of Judgment (Dublin Descriptors 1, 2, 3). The Project Work on real data consists of a report on statistical analysis of empirical data to be conducted in groups of up to three students using the advanced spreadsheet (EXCEL). The Project Work tests the acquisition of Making judgements, Communication Skills, Learning Skills, Digital skills (1, 2, 3), teamwork, time management and development of new strategies and solutions to solve problems. Project Work is assessed with a score up to 1 to be added to the score obtained in the two/only tests, limited to the first exam session.

The final essay is a work in which statistical methods are applied in politics, economics or society. The topic is agreed with the teacher.