What the exam asks
On the exam, you will be given tables of summary statistics (, , minimum, , median, , maximum) for one or more groups and asked to:
- Calculate outlier boundaries (fences) using the rule or the 2-standard-deviation rule and identify whether specific values or a data set contain outliers.
- Explain how adding, removing, or changing an extreme value affects specific summary statistics.
- Compare two or more independent samples using summary statistics in context.
- Justify why one measure of center or variability is preferable to another for a given distribution.
Core ideas
Two rules for identifying outliers
An outlier is a data value that falls unusually far from the bulk of the distribution. AP Statistics uses two formal criteria to flag outliers:
-
The rule (based on quartiles): First find the interquartile range, . Then compute the lower and upper fences:
Resistant vs. nonresistant statistics
A numerical summary is resistant if extreme values (outliers) have little or no effect on its value.
| Measure | Type | Resistant? | Why? |
|---|---|---|---|
| Median | Center | Yes | Depends only on the middle position(s) of ordered data, not the exact magnitudes of extreme values. |
| Mean () | Center | No | Sums every value (), so an extreme value pulls the mean toward itself. |