Teaching code

4S00121

Academic staff

Catia Scricciolo, Cesare Cottonaro

Coordinator

Catia Scricciolo

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/01 - STATISTICS

Period

Primo semestre L dal Sep 22, 2025 al Dec 18, 2025.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course aims to provide the basic techniques of descriptive statistics, probability calculus and statistical inference for undergraduate students in business and economic sciences, who have acquired the necessary preliminary mathematical notions. Overall, these techniques provide the necessary toolkit for the quantitative analysis of processes related to the observation of collective phenomena. From a practical point of view, these techniques are necessary for descriptive, interpretative and decision-making purposes for conducting statistical surveys related to economic and social phenomena. In addition to providing the necessary mathematical statistics apparatus, the course aims at providing conceptual tools for a critical evaluation of the methodologies considered. At the end of the lessons, the student must be able to use the tools learned to conduct statistical analyses relating to economic and social phenomena.

Prerequisites and basic notions

The basic knowledge of mathematics (including limits, derivatives, and integrals) is assumed to be acquired.

Program

a) DESCRIPTIVE STATISTICS
• Introductory concepts: collective phenomena, population and sample; data collection, processing, and classification; qualitative and quantitative variables; statistical sources.
• Types of statistical data: Statistical distributions (simple, double, unit, frequency); graphical representations; histograms.
• Cumulative and reverse cumulative frequencies: Stepwise distribution function for frequency data; continuous distribution function for interval-classed data.
• Measures of central tendency: Arithmetic mean, harmonic mean, geometric mean, power means; median (as first-order center); quartiles, deciles, percentiles, and quantiles; mode.
• Variability and dispersion measures: Range, interquartile range, standard deviation, and variance; variance of linear transformations and mixtures; standardization; relative variability measures (coefficient of variation).
• Raw and central moments.
• Skewness and its measures; kurtosis and its measures.
• Bivariate and multivariate distributions (unit and frequency-based): Arithmetic mean of sums and products of variables; covariance; variance of sums; conditional distributions; independence; chi-square dependence index.
• Statistical interpolation: Least squares method; regression line; linear correlation coefficient; Cauchy-Schwarz inequality; coefficient of determination (R²); total, explained, and residual deviance.
b) PROBABILITY
• Random experiments: sample space; random events and operations; basics of combinatorics.
• Probability spaces: axiomatic definition of probability; interpretations of probability. Conditional probability; product rule; stochastic independence; law of total probability; Bayes’ theorem.
• Random variables: cumulative distribution function; discrete and continuous random variables; transformations; expected value and variance; Markov’s and Chebyshev’s inequalities.
• Discrete distributions: Uniform, Bernoulli, binomial.
• Continuous distributions: Uniform, normal.
• Bivariate discrete random variables: joint probability distribution; marginal and conditional distributions; independence; covariance; Bravais linear correlation coefficient.
• Linear combinations of random variables: sample mean of independent variables; sum of independent normal variables.
• Weak law of large numbers (weak form); Bernoulli’s law of large numbers for relative frequencies; Central Limit Theorem.
c) INFERENTIAL STATISTICS
• Sampling: sample mean, sample proportion, sample variance; Chi-square, Student’s t, and Fisher-Snedecor F distributions.
• Point estimation: unbiasedness, efficiency, and consistency of estimators; estimation of mean, proportion, and variance.
• Interval estimation: Confidence intervals for mean, proportion (large samples), and variance.
• Hypothesis testing: type I and II errors, test power, and p-value; one- and two-tailed tests for mean, proportion (large samples), and variance; comparison of two proportions (large samples), two means, and two variances.
REFERENCE TEXTS
- A. AGRESTI (2022) Metodi statistici di base e avanzati per le scienze sociali. A cura di A. Petrucci e M. Porcu. Perason.
- A. AZZALINI (2001) Inferenza statistica: una presentazione basata sul concetto di verosimiglianza, Seconda edizione.
Springer Verlag Italia.
- E. BATTISTINI (2004) Probabilità e statistica: un approccio interattivo con Excel. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Statistica descrittiva, Collana Schaum's, numero 109. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Calcolo delle probabilita', Collana Schaum's, numero 110. McGraw-Hill, Milano.
- S. BERNSTEIN, R. BERNSTEIN (2003) Statistica inferenziale, Collana Schaum's, numero 111. McGraw-Hill, Milano.
- F. P. BORAZZO, P. PERCHINUNNO (2007) Analisi statistiche con Excel. Pearson, Education.
- N. FREED, S. JONES, T. BERGQUIST (2023) Statistica per le scienze economiche e aziendali. Seconda edizione. ISEDI.
- D. GIULIANI, M. M. DICKSON (2015) Analisi statistica con Excel. Maggioli Editore.
- P. KLIBANOFF, A. SANDRONI, B. MODELLE, B. SARANITI (2010) Statistica per manager, Prima edizione, Egea.
- D. M. LEVINE, D. F. STEPHAN, K. A. SZABAT (2014) Statistics for Managers Using Microsoft Excel, Seventh Edition,
Global Edition. Pearson.
- M. R. MIDDLETON (2004) Analisi statistica con Excel. Apogeo.
- D. PICCOLO (1998) Statistica, Seconda edizione 2000. Il Mulino, Bologna.
- D. PICCOLO (2010) Statistica per le decisioni, Nuova edizione. Il Mulino, Bologna.
EXERCISE BOOKS
- M. R. SEBASTIANI (2022) Esercitazioni di Statistica. Società Editrice Esculapio.
- L. PAGANI (2022) Complementi ed esercizi di Statistica descrittiva e inferenziale. Amon.

Didactic methods

The course includes 84 hours of in-person teaching, consisting of 48 hours of lectures (equivalent to 6 ECTS credits) and 36 hours of practical exercises (equivalent to 3 ECTS credits).
During the course, students are guided on which sections of the textbook to study for each topic. In addition to the 84 hours of instruction, 20 hours of supplementary teaching activities (tutoring) are provided as further academic support.
Lectures, exercises, and tutoring sessions are held in person and are recorded.
All course materials—including lecture notes, exercise materials, tutoring resources, past exam papers, detailed syllabi, exam guidelines, and video recordings—are published on the university’s e-learning platform (Moodle).

Learning assessment procedures

The exam can be taken in two partial written tests or a single comprehensive written test.
EXAM REGISTRATION
Students must register for both partial written tests and the general written test. Students who are not officially registered will not be admitted to take the exam (partial or general).
CONTENTS AND GRADING OF PARTIAL WRITTEN TESTS
First partial test covers the syllabus up to the midterm suspension of lectures. Second partial test covers the remaining part of the syllabus. The second partial test can be taken in only one of the two available winter exam sessions.
If students
- withdraws from the second partial test,
- fails the second partial test, or
- fails the overall exam (final score < 17/30),
they must subsequently take the exam only via the general written test. Each partial test lasts 1 hour and 30 minutes and consists of 20 multiple-choice questions (theoretical and/or applied). Each question is assigned 1 or 2 points based on difficulty, with a maximum achievable score of 31 (=30L).
A minimum score of 17/30 is required to pass each partial test.
CONTENTS AND GRADING OF THE GENERAL WRITTEN TEST
The general written test covers the entire course syllabus and lasts 1 hour and 30 minutes. It consists of 20 questions: 19 multiple-choice (theoretical and/or applied), 1 open-ended question (typically divided into two sub-questions) which may involve: a proof (from either part of the syllabus), a definition, or a problem-solving exercise. Each question is assigned 1 or 2 points, with a maximum achievable score of 31 (=30L). A minimum score of 17/30 is required to pass. Students scoring exactly 17 must take a mandatory oral exam. An optional supplementary oral exam is available for those scoring 18 or higher (in either partial or general tests).
GENERAL RULES
The exam format is the same for attending and non-attending students.
Allowed: Calculator use.
Not allowed: Notes or any other reference materials.

Evaluation criteria

In grading written assignments, primary importance is given to the statistical interpretation of results within the context of the problem. Therefore, it is strongly recommended (where possible) to justify the answers provided and explain the reasoning used to solve the exercises.

Criteria for the composition of the final grade

The overall score for the two partial written tests is calculated as the arithmetic mean of the individual test scores, rounded up.
If an oral exam is taken, the final grade is determined by the arithmetic mean (rounded up) of the scores obtained in the written and oral exams.

Exam language

Italiano