AP Statistics · Unit 1 · Topic 1.6

Describing Distributions Study Lab

To describe a distribution of a quantitative variable, talk about its shape, center, variability, and any unusual features, always in context. Generate samples from five population shapes, add an outlier, and read a model description written from the data.

1. Describe it like a statistician

Every description of a quantitative distribution covers four things, in context: shape, center, variability (spread), and unusual features such as outliers, gaps, and clusters.

Population shape

Controls

Sample size n

Spread Stretch or squeeze the variability.

Graph

MeanMedian

Mean

Median

IQR

Range

Game: name that shape

A mystery sample appears below. Pick the word that best describes its shape.

Mystery sample

2. Key ideas

Shape

Symmetric or skewed

Symmetric: the two halves are near mirror images. Skewed right: a long tail toward larger values. Skewed left: a long tail toward smaller values. Name the skew for the tail, not the peak.

Peaks

Modes

Unimodal distributions have one peak, bimodal have two, and uniform distributions have no clear peak. Two peaks often mean two different groups are mixed together.

Center

Typical value

Report the median for skewed data or data with outliers, and the mean for roughly symmetric data. Give the value with units.

Variability

How spread out

Report the IQR with the median, or the standard deviation with the mean. The range is a quick but non-resistant measure.

Unusual

Outliers, gaps, clusters

Outliers are values that fall outside the overall pattern (check with the 1.5 × IQR rule). Gaps are empty stretches; clusters are groups of values separated by gaps.

Context

Name the variable

“The distribution of call length (minutes) is skewed right with a median of 4.6 minutes…” A description without context loses credit.

3. Shape at a glance

How each shape looks and what it does to the mean and median.

Shape	What you see	Mean vs. median	Example	Report
Symmetric, unimodal	One peak, mirror-image sides	About equal	Adult heights	Mean and SD
Skewed right	Peak on the left, long tail to the right	Mean > median	Incomes, call lengths	Median and IQR
Skewed left	Peak on the right, long tail to the left	Mean < median	Scores on an easy test	Median and IQR
Uniform	Bars about equal height	About equal	Random digits	Mean and SD, or median and IQR
Bimodal	Two peaks	Depends; often between the peaks	Geyser wait times	Describe each cluster

4. On the FRQ

How to earn the points

Use all four parts every time: shape, center, variability, unusual features, with the variable's name and units.
Give numbers, not just words: “median of 22 minutes, IQR of 12 minutes.” Estimates read from a graph are fine if they're reasonable.
When comparing distributions (topic 1.9), use comparison words like “greater than” or “more variable than,” not just two separate lists.
Back up an outlier claim with the 1.5 × IQR rule when you have the quartiles.

Common mistakes

Naming skew by where the peak is. A peak on the left with a tail to the right is skewed right.
Describing a bar chart (categorical data) as skewed or symmetric.
Saying “the range is 20 to 80.” The range is a single number: 80 − 20 = 60.
Leaving out context: “The data are skewed” earns less than “The distribution of phone call lengths is skewed right.”

5. Practice questions

AP-style multiple choice. Pick an answer to see the explanation.

0 / 0 correct

6. Key terms

The vocabulary for topic 1.6. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.