What the exam asks
- Multiple Choice (Section I): Identify the shape of a histogram, stem-and-leaf plot, or dotplot; estimate the median or interquartile range () from a graph; or select the correct statement comparing a claim against a graphical display.
- Free Response (Section II, for example Questions 2 and 4): “Describe the distribution of [variable]” or “Use the graph to justify whether [claim] is supported.” Answers are scored point by point, so address every required feature, in context with units.
Core ideas
1. Shape
Look at the overall pattern of the graphical display (smooth out minor bin-to-bin bumps) and describe two aspects: symmetry/skewness and modality.
| Feature | Term | How to recognize it |
|---|---|---|
| Symmetry / Skewness | Approximately symmetric | The left and right sides are rough mirror images around the center. |
| Skewed right (positively skewed) | The right tail (higher values) is much longer than the left tail; the bulk of the data is on the left. | |
| Skewed left (negatively skewed) | The left tail (lower values) is much longer than the right tail; the bulk of the data is on the right. | |
| Modality / Peaks | Unimodal | Has one clear main peak (mode). |
| Bimodal | Has two distinct peaks (often indicating two subgroups in the sample). | |
| Approximately uniform | Has no distinct peaks; frequencies are roughly equal across all intervals. |
2. Center and Variability
When working from a graph without raw summary statistics, estimate the numerical values of center and variability and state which measure you are using:
- Center: Report the mean () or median. From a histogram or dotplot of observations, you can find the exact bin or value of the median by counting to the ordered observation.