What the exam asks
On the AP Statistics exam, you must be ready to perform four specific tasks from CED Topic 1.9:
- Compare two or more distributions (shown as stacked dotplots, histograms, back-to-back stem-and-leaf plots, or parallel boxplots) across all four features—center, variability, shape, and unusual features—using explicit comparative words and context.
- Justify a claim about two or more groups by citing graphical evidence and numerical summary statistics.
- Calculate and interpret a standardized score (-score) to describe an observation’s relative position.
- Compare -scores to decide which observation is more extreme within a single distribution or across different distributions.
Core ideas
Comparing distributions completely
When the prompt says compare the distributions of a quantitative variable across two or more groups, listing the statistics of Group A in one sentence and Group B in another earns no credit for comparison. You must directly link the groups using comparative phrases (“is greater than,” “is more variable than,” “both are skewed right”) for every component and include the variable and units in context.
| Feature | How to compare across graphs and summaries | Explicit comparative phrases |
|---|---|---|
| Shape | Compare symmetry, skewness (direction of the longer tail), or modality from histograms, dotplots, stem-and-leaf plots, or boxplots. | “Distribution A is skewed to the right, whereas Distribution B is roughly symmetric.” |
| Center | Compare medians (especially from boxplots or skewed data) or means. Cite the values. | “The median commute time for Route 1 () is higher than for Route 2 ().” |
| Variability | Compare interquartile ranges (), standard deviations (), or ranges. Cite the values. | |
| Unusual features | Mention outliers, gaps, or clusters for each group (or state that neither group has them). | “Route 2 has two high outliers above , while Route 1 has no outliers.” |