The comparison, in context
To compare two distributions of a quantitative variable, address shape, outliers, center, and spread (SOCS) and use comparison words like "greater than" or "less variable than." Pick two groups, shift and stretch one of them, and read a full comparison written in context.
Both graphs use the same scale, so you can compare them directly.
The comparison, in context
Each statement compares the two groups from the first preset. Is it a complete, correct comparison? Decide, then read why.
Describe shape, outliers, center, and spread for both groups. Missing any one of them is the most common way to lose credit on a comparison question.
"Group A's median is 7 hours and group B's median is 6 hours" is a list. "The median for group A (7 hours) is greater than the median for group B (6 hours)" is a comparison. AP requires the comparison.
Always say what is being measured and in what units: "sleep per night (hours) for 9th graders," not just "group A's data."
Comparative dotplots, parallel boxplots, back-to-back stemplots, and stacked histograms with a common scale let you see differences in center and spread at a glance.
If either group is skewed or has outliers, compare medians and IQRs. If both are roughly symmetric with no outliers, means and standard deviations work.
A higher center does not mean every value is higher. Note how much the two distributions overlap; it tells you how consistent the difference is.
Turn each weak sentence into one that would earn full credit.
| Feature | Weak (no credit) | Strong (credit) |
|---|---|---|
| Shape | "Both are skewed." | "The distribution of commute times for city workers is skewed right, while the distribution for suburban workers is roughly symmetric." |
| Outliers | "There is an outlier." | "City workers have one high outlier at 70 minutes; suburban workers have no outliers." |
| Center | "A's median is 22 and B's median is 30." | "The median commute for suburban workers (30 min) is greater than the median for city workers (22 min)." |
| Spread | "A is more spread." | "Commute times for city workers are more variable (IQR = 15 min) than for suburban workers (IQR = 8 min)." |
| Overall | "B is bigger." | "Suburban workers typically have longer, more consistent commutes, although the two distributions overlap a lot." |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 1.9. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.