Statistics (2018/2019)

Course code
Name of lecturers
Francesca Rossi, Veronica Cicogna
Francesca Rossi
Number of ECTS credits allocated
Other available courses
Academic sector
Language of instruction
primo semestre lauree triennali dal Sep 17, 2018 al Jan 11, 2019.

Lesson timetable

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Learning outcomes

This module provides 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 undergraduate calculus. In general, this module aims to offers a toolkit to investigate collective phenomena, starting from conducting a simple descriptive analysis to performing more formal hypothesis testing. The theoretical techniques students will acquire by the end of the course are necessary for descriptive, interpretative and decision-making purposes, as well as, more generally, for carrying out statistical studies related to economic and social phenomena. In addition to offering the necessary mathematical apparatus, the course also aims at providing the conceptual tools for a critical evaluation of the methodologies considered.


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; 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; method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficiente; deviance residual and deviance explained; multivariate frequency distributions; conditional distributions; chi-squared index of dependence; index of association C.

Probability: 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 distribution; Bernoulli distribution; binomial distribution; continuous uniform distribution; 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 random variables; weak law of large numbers; Bernoulli’s law of large numbers for relative frequencies; central limit theorem.

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.

The course consists of a series of lectures (56 hours) and of twelve exercise classes (24 hours).
All classes are essential to a proper understanding of the topics of the course.
The working language is Italian.

Reference books
Author Title Publisher Year ISBN Note
G. Cicchitelli, P. D'Urso, M. Minozzo Statistica: principi e metodi (Edizione 3) Pearson Italia, Milano 2018 9788891902788

Assessment methods and criteria

The final exam consists of a two-hours written exam paper containing both practical exercises and theoretical definitions and derivations. Students are allowed to use a calculator, but no other material (such as books, notes, etc.). There is no compulsory oral examination, but students who get a mark of at least 15/18 have the option of integrating their mark by means of an interview. The oral examination offers the possibility of gaining or losing up to three marks compared to the result of their script. Students are expected to show an id (or student's card) in order to sit the exam.

An intermediate examination paper on the first part of the program is planned and students can take it on a voluntary basis. Students who successfully pass the intermediate examination have the option of taking a similar paper on the second part of the module during the exam session immediately after the end of the course, rather than sitting the full final exam paper. The two partial examination will have the same weight on the final mark, and each of them has to be passed with a mark of at least 8/30. Accurate notification about the topics covered in the first partial examination will be posted on the course webpage in due course. Students are encouraged to take the intermediate examination, not only in view of splitting the examinable material in two parts, but also and especially to self-assess progresses and weaknesses in a timely and efficient manner.

Student opinions - 2017/2018