Statistics (2017/2018)

Course partially running (all years except the first)

Course code
Name of lecturers
Marco Minozzo, Mauro Mussini
Marco Minozzo
Number of ECTS credits allocated
Academic sector
Language of instruction
Primo Semestre Triennali dal Sep 18, 2017 al Jan 12, 2018.

Lesson timetable

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Learning outcomes

The course aims to provide the basic techniques of descriptive statistics, probability and statistical inference to undergraduate students in economic and business sciences. Prerequisite to the course is the mastering of a few basic mathematical concepts such as limit, derivative and integration at the level of an undergraduate first year introductory course in calculus. Overall, these techniques provide the necessary toolkit for quantitative analysis in the processes related to the observation and understanding of collective phenomena. From a practical point of view, they are necessary for descriptive, interpretative and decision-making purposes and for conducting statistical studies related to economic and social phenomena. In addition to providing the necessary mathematical apparatus, the course also aims at providing the conceptual tools for a critical evaluation of the methodologies considered.


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 percentiles.
• Fixed-base indices and chain indices; Laspayres and Paasche indices.
• 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; index of association C; Simpson’s paradox.
• Method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficient; explained deviance and residual deviance.

b) Probability

• Random events, probability spaces and event trees; combinatorics.
• Conditional probability; independence; Bayes theorem.
• Discrete and continuous random variables; distribution function; expectation and variance; Markov and Tchebycheff inequalities.
• Discrete uniform distributions; Bernoulli distribution; binomial distribution; Poisson distribution; geometric distribution.
• Continuous uniform distributions; normal distribution; exponential distribution.
• 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 and Gaussian random variables.
• 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-t distribution; Snedecors-F distribution.
• Point estimates and estimators; unbiasedness; efficiency; consistency; estimate of the mean, of a proportion and of a variance.
• 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 in two means, two proportions (large samples) and two variances.


- G. CICCHITELLI, P. D’URSO, M. MINOZZO (2018), Statistica: principi e metodi, Terza edizione, Pearson Italia, Milano.

Reading list

- 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 probabilità, 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, 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.

Study guide

Detailed indications, regarding the use of the textbook, will be given during the course. Supporting material (written records of the lessons, exercises with solutions, past exam papers with solutions, etc.) is available on the E-learning platform of the University.


Students are supposed to have acquired mathematical knowledge of basic concepts such as limit, derivative and integral.

Teaching methods

Course load is equal to 80 hours: 56 lecture hours (equal to 7 ECTS) and 24 exercise hours (equal to 2 ECTS). All classes are essential to a proper understanding of the topics of the course. The working language is Italian.

Exercise sessions

Exercise sessions are integral part of the course and are necessary to an adequate understanding of the topics.

Tutoring activities

In addition to lessons and exercise hours, before each exam session there will be tutoring hours devoted to revision. More detailed information will be available during the course.

Reference books
Author Title Publisher Year ISBN Note
D. Giuliani, M. M. Dickson Analisi statistica con Excel Maggioli Editore 2015 8838789908
M. R. Middleton Analisi statistica con Excel Apogeo, Milano 2004
F. P. Borazzo, P. Perchinunno Analisi statistiche con Excel Pearson, Education 2007
S. Bernstein, R. Bernstein Calcolo delle Probabilita', Collana Schaum's, numero 110. McGraw-Hill, Milano 2003
A. Azzalini Inferenza Statistica: Una presentazione basata sul concetto di verosimiglianza (Edizione 2) Springer Verlag Italia 2001 9788847001305 Laurea in Matematica Applicata
E. Battistini Probabilità e statistica: un approccio interattivo con Excel McGraw-Hill, Milano 2004
D. Piccolo Statistica Il Mulino 2000 8815075968
S. Bernstein, R. Bernstein Statistica descrittiva, Collana Schaum's, numero 109 McGraw-Hill, Milano 2003
S. Bernstein, R. Bernstein Statistica inferenziale, Collana Schaum's, numero 111. McGraw-Hill, Milano 2003
D. Piccolo Statistica per le decisioni Il Mulino 2004 8815097708
P. Klibanoff, A. Sandroni, B. Moselle, B. Saraniti Statistica per manager (Edizione 1) Egea 2010 9788823821347
G. Cicchitelli, P. D'Urso, M. Minozzo Statistica: principi e metodi (Edizione 3) Pearson Italia, Milano 2018 9788891902788 Libro di testo
D. M. Levine, D. F. Stephan, K. A. Szabat Statistics for Managers Using Microsoft Excel, Global Edition (Edizione 7) Pearson 2014 0133061817

Assessment methods and criteria

The final exam consists of a written test (of two hours and 30 minutes) with classical exercises and multiple choice questions. For the written test, students can use a scientific calculator; any other material (books, notes, etc.) is forbidden. To pass the exam, students must receive at least 15 out of 30 in both parts of the written test. If the final mark (that is the average of the grades obtained in the two parts of the written test) is less the 18 out of 30, the student is required to sit for an oral examination. Contents, assessment methods and criteria are the same for all students and do not depend on the number of classes attended.

A noncompulsory intermediate test on the first part of the program (typically on descriptive statistics and a part of probability) is planned for the beginning of November. The passing of this intermediate test can entail an increase of at most three points of the result obtained in the written test (if the written test is taken and passed in one of the two winter examination sessions).

Teaching aids