The teaching is organized as follows:

Learning outcomes

The course is intended to provide an introduction to Descriptive Statistics, Probability and Inferential Statistics. The course is for 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. The statistical techniques that will be illustrate in the course are intended to provide instruments useful for description and interpretation of collective data. From a practical point of view, methods are necessary for interpreting official statistics and for realizing statistical studies of economical and social phenomena. The course is also intended to provide instruments for a critical analysis of the methodology.

Program

a) Descriptive Statistics

Introduction; data collection; population, sample, statistical unit; survey; questionnaire; data classification; data types; statistical sources.
Statistical data; matrix data; types of frequency distributions; graphical representations.
Cumulative frequency; cumulative distribution function.
Measures of central tendency; arithmetic mean, geometric mean and harmonic mean; properties of the arithmetic mean; quadratic and cubic mean; mood; median; quartiles and percentiles.
Variability and measures of dispersion; variance and standard deviation; coefficient of variation.
Moments; indices of skewness and kurtosis.
Fixed and varying base indices; Laspayres and Paasche indices.
Double and multivariate distributions; frequency tables; covariance; variance of the sum of more variables; conditional distributions; conditional mean and variance;
scatterplots; covariance; variance of the sum of more variables; chi-squared index of dependence; index of association C.
Least squares metodo; scatterplot; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficiente; regression and residual deviance.

b) Probability

Deterministic and probabilistic models; events, probability spaces and event trees.
Combinatorics.
Definition and probability; probability function; theorems; 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; Poisson distribution; continuous uniform distribution; normal distribution; multivariate discrete random variables; joint probability distribution; marginal and conditional probability distributions; independence; expectation and covariance; correlation coefficient; conditional expectation and variance.
Linear combinations of random variables; average of random variables; sum of independent normals.
Weak law of large numbers.
Central limit theorem.

c) Inferential Statistics

Introduction; sample and sampling variability; sample statistics and sampling distributions.
Point estimates and estimators; unbiasedness; efficiency; consistency; estimate of the mean, of a proportion and of a variance.
Confidence intervals; intervals for a mean, for a proportion (large samples) and for a variance.
Hypothesis testing; first- and second-type errors and power of a test; 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.

Book

- G. CICCHITELLI (2012), Statistica: principi e metodi, Seconda edizione, Pearson Italia, Milano.

Other books

- D. PICCOLO (1998), Statistica, Seconda edizione 2000. Il Mulino, Bologna.
- D. PICCOLO (2010), Statistica per le decisioni, Nuova edizione. Il Mulino, Bologna.
- M. R. MIDDLETON (2004), Analisi statistica con Excel. Apogeo.
- E. BATTISTINI (2004), Probabilità e statistica: un approccio interattivo con Excel. McGraw-Hill, Milano.
- F. P. BORAZZO, P. PERCHINUNNO (2007), Analisi statistiche con Excel. Pearson, Education.

Details

The course consists of a series of lectures (56 hours) and of twelve exercise classes (24 hours). The working language is Italian.

It is assumed that students have a basic knowledge of mathematics, in particular about limits, derivation methods an integration techniques.

The material which will be used during the exercise lessons will be made available online (e-learning).

Examination Methods

The examination consists of two separate tests, one with a series of questions, and one with some exercises. The total examination will take about 2 hours and 30 minutes.
The examination is considered successful if the candidate has passed both the two written tests: students must receive at least 16 out of 30 in both written tests, and the final average score has to be at least equal to 18/30. Final scores equal to 16/30 or 17/30 allow to face an oral and optional examination.
No books or personal material is allowed during the examination. Only the calculating machine is allowed. Material to use for evaluating the quantiles or the probabilities of statistical distributions will be made available by the teacher during the examination. The students are required to attend the examination with the identity card or a similar document.