The course is intended to provide an introduction to Descriptive Statistics, Probability, and Inferential Statistics. The course is for students in Economics and Business Administration. 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 illustrated 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 performing statistical studies of economical and social phenomena. The course is also intended to provide instruments for a critical analysis of the methodology.
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 two or more than two variables; conditional distributions; conditional mean and variance; scatterplots; covariance; variance of the sum of two or more than two variables; chi-squared index of dependence; index of association C.
Least squares metod; scatterplot; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficient; regression and residual deviance.
Deterministic and probabilistic models; events, probability spaces and event trees.
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.
- G. CICCHITELLI (2012), Statistica: principi e metodi, Second edition, Pearson Italia, Milano.
- D. PICCOLO (1998), Statistica, Second edition 2000. Il Mulino, Bologna.
- D. PICCOLO (2010), Statistica per le decisioni, New edition. 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.
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, and integration techniques.
The material which will be used during the exercise lessons will be made available online (e-learning).
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 students to face an oral and optional examination.
No books or personal material are 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.
In mid-November 2014, students have the opportunity to take an intermediate examination on the first part of the program. The intermediate examination (about 1 hour) consists in a series of questions. The final positive score will be considered during the two Winter examination sessions. The final score of the intermediate examination can provide an increase of at most three points of the (positive) result of the written examination of the Winter sessions.
|Outcomes Exams||Outcomes Percentages||Average||Standard Deviation|
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Data from AA 2014/2015 based on 181 students. I valori in percentuale sono arrotondati al numero intero più vicino.