The course aims at providing 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 introductory course in calculus. Overall, these techniques provide the necessary toolkit for quantitative analysis in 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 when carrying out statistical studies related to economic and social phenomena. In addition to providing the necessary mathematical apparatus, the course aims at providing 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.
|G. Cicchitelli, P. D'Urso, M. Minozzo||Statistica: principi e metodi (Edizione 3)||Pearson Italia, Milano||2018||9788891902788|
Students will be evaluated on both practical exercises and theoretical definitions and derivations. Students are allowed to use a calculator and statistical tables, but no other material (such as books, notes, etc.).
Students are expected to show an id (or student's card) in order to sit the exam.
Students will sit a written examination, either in the classroom or via Zoom, at their discretion. Students that will sit the exam via Zoom should expect a multiple choice quiz, followed, only for those that are successful in the quiz, by a very brief oral interview to discuss the quiz answers. For both classroom and Zoom exam, the past exam papers will be an important reference of what students should expect.