B019494 - STATISTICS

italian

Module I introduces students to the topic of collecting and processing statistical data, with particular reference to the economic-social field of application.

The topics covered are the following.
Design and implementation of a statistical survey: setting goals, choosing the population and characters; explanation of the measurement system; identification of technical means for data collection. The drafting of a questionnaire. Data quality control.
Distributions of a character and its representation. From the sequence of observed modalities to frequency distributions. Absolute, relative, cumulative frequencies. Tabular representations. Graphic representations.
Summary of the distribution of a character - The means: arithmetic and geometric means; averages deduced from equivalence conditions; trimmed mean; median, mode, percentiles.
Summary of the distribution of a character - Variability: indices based on the deviation from the mean; other indices of variability; Concentration. Chebyshev's theorem. Box Plot.
Analysis of the association between two characters: double frequency distributions. Dependence, independence, interdependence. Measurements of association for qualitative characters. Measurements of association of a quantitative from a qualitative character. Interdependence between quantitative characters: covariance, correlation and regression.
Probability - Axiomatic approach: events and event algebra; the axioms; conditional probability and independence. Bayes' theorem.
Random variables and probability distributions: concept of random variable; discrete and continuous random variables; expected value and variance of a random variable. Discrete uniform distribution. Distribution of Beroulli. Binomial distribution. Continuous uniform distribution. Normal Distribution. Student's t-distribution. Central limit theorem.
Sampling and sample distributions: sampling from finite populations; simple random sample; sampling from infinite populations. Sample statistics and sample distributions. The distribution of the sample mean. Point estimate: concept of estimate and estimator; correct estimators; efficient estimators. Point estimate of the mean of a population. Point estimate of the proportion of a population. Estimation of the variance of a population.
Interval estimation: concept of estimation by interval and confidence interval. Confidence interval for the mean. Confidence interval for the proportion.
Simple linear regression: functional relationship between two variables. Model specification. Point estimate of the regression coefficients. Decomposition of the total variance