Chapter 2: Modeling Distributions of Data

Students learn to calculate and interpret the mean and median as measures of center, understanding how each responds differently to skewed distributions and extreme values, which determines when to use each measure appropriately. The chapter then develops understanding of data spread through the range, interquartile range, and standard deviation, emphasizing that variability must always be interpreted alongside center to convey a complete picture of the data. The five-number summary encapsulates these ideas by presenting the minimum, first quartile, median, third quartile, and maximum, which can be visualized as a boxplot that immediately reveals the shape and spread of a distribution. Outlier detection using the 1.5 times the interquartile range rule provides a formal method for identifying unusual observations. The chapter shifts focus to mathematical modeling by introducing density curves as smooth representations of overall distribution patterns. The Normal distribution, a symmetric bell-shaped model defined by its mean and standard deviation, becomes the central focus, with students learning to apply the 68-95-99.7 rule to estimate proportions within standard deviation intervals. The standard Normal distribution and z-score transformation allow students to standardize any observation for comparison across different data sets and contexts. Using standard Normal tables or technology, students find proportions and percentiles, while Normal probability plots provide a graphical tool to assess whether a data set reasonably follows a Normal model. Together, these concepts equip students with both descriptive and inferential tools for analyzing quantitative data precisely and appropriately.