Data organization: qualitative data; quantitative data; paired data.

Descriptive statistics: measures of center; measures of variation; sample percentiles; skewness; kurtosis; sample covariance and correlation.

Probability: sample space and events; union and intersection of events; complement of an event; Venn diagrams; basic properties of probability; joint and marginal probabilities; conditional probability and independence; Bayes’ theorem; counting principles.

Random variables and probability distributions: probability density functions and cumulative distribution functions; some common discrete distributions (Bernoulli; discrete uniform; binomial; Poisson); joint, marginal and conditional distributions; measures of central tendency: measures of variability; standardized random variables; some useful continuous distributions (uniform, normal, log-normal, Chi-square, Student’s t, F); analysis of conditional distributions; analysis of joint distributions.

Mathematical statistics and inferential statistics: statistical inference and sampling: random sampling; parameters, estimators and estimates; finite sample properties of estimators (unbiasedness and efficiency); large sample properties of estimators (consistency; law of large numbers and properties of the probability limit; central limit theorem and asymptotic normality).

Confidence Intervals (CIs) and hypothesis testing: CIs for one population mean; critical values; margin of error; asymptotic confidence intervals; Type I and II error probabilities, size and statistical power of a test; one-tailed and two-tailed tests for one population mean; p-value approach to hypothesis testing; pooled and non-pooled two-sample t tests for inference on two population means using independent samples; inference for population proportions.

An introduction to non-parametric statistics: kernel density estimator; rank-based tests (sign test; Wilcoxon signed-rank test; Mann-Whitney test; Kruskal-Wallis test).