Scientific Disciplinary Sector (SSD)
SECS-S/01 - STATISTICS
Primo semestre (lauree) dal Sep 19, 2022 al Jan 13, 2023.
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.
a) DESCRIPTIVE STATISTICS
• Data collection and classification; data types.
• Frequency distributions; histograms and charts.
• Measures of central tendency; arithmetic mean, geometric mean and harmonic mean; median; quartiles and
• Variability and measures of dispersion; variance and standard deviation; coefficient of variation.
• Moments; indices of skewness and kurtosis.
• Multivariate distributions; scatterplots; covariance; variance of the sum of more variables.
• Multivariate frequency distributions; conditional distributions; chi-squared index of dependence; Simpson’s
• Method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation; Cauchy-Schwarz
inequality; R^2 coefficient; total, explained and residual deviance.
• Random experiments; sample space; random events and operations; combinatorics.
• Conditional probability; independence; Bayes' theorem.
• Discrete and continuous random variables; distribution function; expectation and variance; Markov and
Tchebycheff's inequalities. Special discrete distributions: uniform, Bernoulli, Binomial, Poisson and geometric.
Special continuous distributions: continuous uniform, Gaussian, exponential.
• Multivariate discrete random variables; joint probability distribution; marginal and conditional probability
distributions; independence; covariance; correlation coefficient.
• Linear combinations of random variables; average of independent random variables; sum of independent, Gaussian
• Weak law of large numbers; Bernoulli’s law of large numbers for relative frequencies; central limit theorem.
c) INFERENTIAL STATISTICS
• Sample statistics and sampling distributions; Chi-square distribution; Student's t distribution; Snedecor's F
• Point estimates and estimators; unbiasedness, efficiency, consistency; estimate of a mean, of a proportion, of a
• Confidence intervals for a mean, for a proportion (large samples) and for a variance.
• Hypothesis testing; one and two tails tests for a mean, for a proportion (large samples) and for a variance;
hypothesis testing for differences between two means, two proportions (large samples) and two variances.
- A. AZZALINI (2001) Inferenza statistica: una presentazione basata sul concetto di verosimiglianza, 2nd Ed.,
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.
- D. GIULIANI, M. M. DICKSON (2015) Analisi statistica con Excel. Maggioli Editore.
- P. KLIBANOFF, A. SANDRONI, B. MODELLE, B. SARANITI (2010) Statistica per manager, 1st Ed., Egea.
- D. M. LEVINE, D. F. STEPHAN, K. A. SZABAT (2014) Statistics for Managers Using Microsoft Excel, 7th Ed.,
Global Edition. Pearson.
- M. R. MIDDLETON (2004) Analisi statistica con Excel. Apogeo.
- D. PICCOLO (1998) Statistica, 2nd Ed. 2000. Il Mulino, Bologna.
- D. PICCOLO (2010) Statistica per le decisioni, New Ed. Il Mulino, Bologna.
Course load is equal to 84 hours: the course consists of 48 lecture hours (equal to 6 ECTS credits) and of 36 exercise hours (equal to 3 ECTS credits).
A detailed syllabus will be made available at the end of the course on the e-learning platform.
Students are supposed to have acquired math knowledge of basic concepts like limit, derivative and integral.
Exercise sessions are integral part of the course and necessary to adequate understanding of the topics.
There will be optional tutoring hours devoted to exercises during the course and before exam sessions. More detailed information will be made available in due course.
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.
Learning assessment procedures
The exam can be passed through two partial written tests or one general written test.
Contents, assessment methods and criteria for partial written tests
The first partial written test focuses on the part of the program explained until the break at the end of October, typically on Descriptive Statistics and part of Probability (cf. the program of the course). The second partial written test focuses on the rest of the program. The topics of the program on which each partial written test is based will be defined in detail in due course. The bonus earned by the student when passing the first partial written test can be used to access the second partial written test in ONLY ONE of the two exam sessions of January and February. In case of
- student's withdrawal during the second partial written test
- failing of the second partial written test
- failing of the total exam due to a final exam grade less than 18/30 (cf. assessment methods and criteria for partial written tests)
the exam can be subsequently taken ONLY through a general written test.
Both partial written tests include exercises and theoretical questions. Each partial written test is passed if the score is greater than or equal to 15/30. If both partial written tests are passed, the final exam mark results from the weighted average (eventually rounded up to the least greater integer) of the grades obtained in the single partial written tests. The exam is passed if this average is greater than or equal to 18/30. If the total score obtained is greater than or equal to 15 and less than 18, the student may take an additional oral test. There is the possibility to take an optional oral test for those who have obtained a score greater than or equal to 18/30. Date and time of the oral test will be promptly communicated after the written test.
Contents, assessment methods and criteria for general written test
The general written test covers all topics of the program and includes exercises and theoretical questions. The exam is passed if the score is greater than or equal to 18/30. If the grade earned is greater than or equal to 15 and less than 18, the student may take an additional oral test. There is the possibility to take an optional oral test for those who have obtained a score greater than or equal to 18/30. Date and time of the oral test will be promptly communicated after the written test.
Contents, assessment methods and criteria are the same for attending and non-attending students.