Measures of Variability: Range, Interquartile Range, and MAD

Formulate statistical questions, compare census and sampling methods, collect categorical and numerical data, and organize information into frequency tables with grouped intervals.

Construct and interpret dot plots, ordered stem-and-leaf plots, bar charts, and line graphs to display and analyze single-variable and time-series data.

Construct and interpret histograms, circle graphs, and box-and-whisker plots, and critically detect misleading graphical distortions.

Calculate and interpret the mean, median, and mode, evaluate the effect of outliers and skewness, and describe distribution symmetry, clusters, and gaps.

Calculate and interpret measures of spread including the range, interquartile range (IQR), and mean absolute deviation (MAD), comparing data sets comprehensively.

Quantify probability between 0 and 1, calculate theoretical probabilities of simple and compound events, and construct sample spaces using lists, grids, and tree diagrams.

Conduct empirical trials and digital simulations, calculate relative frequencies, compare experimental results with theoretical models, and explain the law of large numbers.