Combinatorics and Counting Techniques

Analyze univariate quantitative data by calculating and interpreting measures of central tendency, position, dispersion, and evaluating frequency distributions.

Quantify, interpret, and evaluate bivariate numerical associations using scatter plots, sample covariance, and Pearson's correlation coefficient.

Master counting principles, permutations, and combinations to quantify outcomes in complex multi-stage probabilistic systems.

Construct formal sample spaces and calculate probabilities for simple, complementary, mutually exclusive, and compound events.

Evaluate conditional probabilities, test for statistical independence, and compute revised probabilities using the Law of Total Probability and Bayes' Theorem.

Design valid comparative experiments and representative random sampling protocols while mitigating bias and confounding variables.

Evaluate published reports, public opinion polling data, deceptive graphics, and common statistical fallacies to draw sound inferential conclusions.