AP Statistics · Exam guide
AP Statistics Describing Data: Shape, Center, Spread, and Outliers in Context
Almost every statistics exam answer that describes data uses four words: shape, center, spread, and unusual features, all in context. A description that leaves out the context earns less credit, even when the numbers are right. This guide gives a sentence pattern and a checked example.
The four parts of a description
| Part | What to say | Tools |
|---|---|---|
| Shape | Symmetric, skewed right, skewed left, unimodal, bimodal. | Histogram, dotplot, stemplot |
| Center | The median for skewed data, the mean for roughly symmetric data. | Median, mean |
| Spread | The interquartile range or range for skewed data, the standard deviation for symmetric data. | IQR, standard deviation, range |
| Unusual features | Outliers, gaps, clusters. | 1.5 times IQR rule, a graph |
A worked example
Twelve students recorded the number of hours they spent on a project: 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 25. Describe the distribution.
The median is \(5.5\) hours, and the mean is about \(7.08\) hours. The quartiles are \(Q_1 = 4\) and \(Q_3 = 7.5\) (the medians of the lower and upper halves), so \(IQR = 3.5\). The upper fence is \(Q_3 + 1.5(IQR) = 7.5 + 5.25 = 12.75\), and the lower fence is \(4 - 5.25 = -1.25\). The value 25 is above the upper fence, so it is an outlier.
It gives no context and does not compare the mean and median or say why the outlier matters.
It names the context, gives the center and spread, justifies the outlier with numbers, and explains the mean versus the median.
Mean versus median
A single large value pulls the mean toward it but barely moves the median. When a distribution is skewed or has an outlier, report the median and IQR. When it is roughly symmetric with no outliers, the mean and standard deviation are fine.
Comparing two distributions
- Compare shape, center, and spread, using comparison words: "larger than," "more variable than."
- Give numbers for both groups in the same sentence.
- Say what the comparison means in the context.
Common mistakes
- Describing the data without naming the variable or the context.
- Using a mean and standard deviation for a skewed distribution with an outlier.
- Saying a value is an outlier without a rule or numbers.
- Writing about two groups separately without comparing them.
Frequently asked questions
Which quartile method does the exam use?
The usual method is the median of each half of the data. A calculator may give slightly different quartiles for some data sets.
Do I always need to test for outliers?
When asked to identify outliers, show the fences with numbers.
What is the difference between standard deviation and IQR?
Both measure spread. The IQR resists outliers, and the standard deviation does not.
What does skewed right mean?
The tail on the right side is longer, so a few large values pull the mean above the median.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Statistics course ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a 10-problem practice set with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Statistics course Free lessons and lesson list
More AP Statistics guides (8)
Start here
Free-response and writing
- AP Statistics Inference for Proportions Explained: Intervals and Tests with a Worked Example
- AP Statistics Inference for Means Explained: The One-Sample t Test and Checking Conditions
- AP Statistics Chi-Square Test Explained: Homogeneity and Independence with a Worked Example
- AP Statistics Regression Questions Explained: Interpreting Slope, r-Squared and Residuals
- AP Statistics Sampling and Experiments: Bias, Random Samples, and Good Design
- AP Statistics Probability and Random Variables: Expected Value, Binomial, and Normal
Multiple choice
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