Measures of Variability and Spread

Understand how random sampling generates representative data, identify sources of bias, and use sample statistics to make valid inferences about population parameters.

Acquire, classify, organize, and construct accurate graphical representations of discrete and continuous numerical data sets.

Calculate and interpret mean, weighted mean, median, and mode, and evaluate which center best represents skewed versus symmetric data sets.

Calculate and interpret measures of dispersion including range, interquartile range (IQR), mean absolute deviation (MAD), and sample variance.

Compare two numeric distributions visually and numerically, quantifying center separation as a multiple of variability to draw informal comparative inferences.

Quantify likelihood between 0 and 1, calculate theoretical probabilities of simple events and complements, and verify the Law of Large Numbers through simulations.

Find probabilities of compound events using organized lists, two-way grids, tree diagrams, simulations, and the Fundamental Counting Principle.