Teaching code

4S00121

Academic staff

Claudia Di Caterina, Giovanna Caramia

Coordinator

Claudia Di Caterina

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/01 - STATISTICS

Period

Primo semestre L dal Sep 23, 2024 al Jan 10, 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

Basic notions of mathematics (including limits, derivatives, integrals).

Program

1) Descriptive statistics
• Introductory concepts, population and sample, qualitative and quantitative characters
• Types of statistical data, statistical distributions (simple, double, unitary, frequency), graphical representations, histogram
• Cumulative frequencies, step or continuous distribution function
• Location indexes: arithmetic mean, harmonic mean, geometric mean, median, quartiles, deciles, percentiles and quantiles, mode
• Variability indexes: range, interquartile range, simple mean deviations, standard deviation and variance; variance of a linear transformation, standardization; relative indexes of variability: the coefficient of variation
• Indexes of asymmetry and kurtosis
• Double, unitary and frequency distributions; arithmetic mean of the sum of several variables and of the product of two variables; covariance and variance of the sum of several variables; conditional distributions; independence and chi-square dependence index
• Statistical interpolation: least squares method and least squares line, linear correlation coefficient and coefficient of determination R^2; total, explained and residual deviance
2) Probability
• Random experiments, sample space, tree diagrams, random events and operations between events, elements of combinatorial calculus
• Algebras and sigma-algebras, probability spaces, axiomatic definition of probability and its interpretations
• Conditional probability, product law, stochastic independence between events, total probability formula and Bayes' theorem
• Discrete and continuous random variables, distribution function, transformations of random variables, expected value and variance
• Notable discrete distributions: uniform, Bernoulli, binomial
• Notable continuous distributions: uniform and normal
• Discrete double random variables: joint probability distribution, marginal and conditional probability distributions, independence between random variables, covariance, Bravais correlation coefficient
• Linear combinations of random variables, sample mean of independent random variables, sum of independent normal random variables
• (Weak) law of large numbers, Bernoulli's law of large numbers for relative frequencies, central limit theorem
3) Inferential statistics
• Probabilistic samples, sample mean, sample relative frequency, sample variance, chi-squared sample distributions, Student's t
• Point estimate, correctness, efficiency and consistency of the estimators; estimation of mean, proportion, variance
• Interval estimate (confidence interval) for mean, proportion (large samples), variance
• Hypothesis tests: observed power and significance level, one-tailed and two-tailed tests for the mean, for the proportion (large samples) and for the variance; comparison between two means

Bibliography

Didactic methods

The course includes 84 hours of lessons, including lectures and exercise sessions. All lectures and exercise sessions are essential for an adequate understanding of the topics covered, as well as individual study. During the course, for each specific topic, the parts of the textbook to be studied are indicated. In addition to the scheduled course hours, several hours of tutoring are also provided as further training support.
All lectures and exercise sessions are held in person. It is advisable to attend the lessons and exercise sessions, taking notes regularly. All the teaching material related to the course (lecture notes, exercises, past exam assignments etc.) is published on the University's E-learning platform (Moodle).

Learning assessment procedures

The final exam is written and consists of three exercises with open questions, both theoretical and practical, on the topics covered in the course. It is allowed to consult a formulary written on a double-sided A4 sheet and the statistical tables, as well as the use of a scientific calculator.
An midterm test is scheduled in November, on about half of the course program. The result, if passed, is added to that of the second partial test taking place with the first exam of the winter session. In each partial test, the exam may include multiple choice questions and the formulary must be prepared on only one A4 side.

Evaluation criteria

Rather than assessing the correctness of the individual numerical results, in the correction of the test primary importance is given to their statistical interpretation within the problem and to the solution of the proposed exercises. Justifying every answer and commenting on the adopted procedures is therefore strongly recommended.

Criteria for the composition of the final grade

The final mark coincides with the score in the final exam, or with the sum of the two partial scores (if both are above a minimum threshold).

Exam language

Italiano