How to describe a distribution (and get full credit)

The four features a full-credit description names

The AP course asks for four things when you describe the distribution of one quantitative variable: shape, center, variability (also called spread), and any unusual features such as outliers, gaps, or clusters. All four have to appear in context, which means naming the variable, the group that was measured, and the units.

The College Board is blunt about where students lose points here. Many write out an acronym like SOCS and then never explain the pieces, and unusual features get skipped most often. A response that covers only the center is scored as incomplete.

So treat the four features as a checklist you write out in full sentences, not a mnemonic you recite. This is topic 1.6 Descriptions for One Quantitative Variable Distributions in Unit 1.

A sentence frame you can reuse

Four features, four sentences. Fill in the blanks and you have a complete answer every time.

1. Shape. The distribution of [variable] for [the group measured] is [skewed to the right / skewed to the left / roughly symmetric], with [one peak / two peaks].
2. Center. The [median / mean] [variable] is about [value] [units].
3. Variability. The [IQR / range / standard deviation] is about [value] [units].
4. Unusual features. There is [an outlier at (value) (units) / a gap between (a) and (b) / a cluster near (value)], or: there are no apparent outliers, gaps, or clusters.

The frame forces the two things a grader is scanning for: a number with units in every sentence, and the variable named at least once. If a feature genuinely is not present, say so out loud. Writing that there are no apparent outliers is an answer, while saying nothing about outliers is a hole in the response.

Partial credit and full credit on the same histogram

Here is a histogram of the amount each of 40 shoppers spent at one farmers market stall, written as a frequency table.

A typical partial-credit answer: "The distribution is skewed right. The center is the median and the spread is the range. There are a few outliers on the right."

A full-credit answer: "The distribution of amounts spent by these 40 shoppers is skewed to the right, with a single peak in the 10 to 20 dollar bin. The median falls in that same bin (the 20th and 21st values both land there), so a typical shopper spent roughly 15 dollars. Amounts run from 0 to 70 dollars, a range of about 70 dollars, and most of the data is packed below 30 dollars. There is a gap from 50 to 60 dollars, and the 2 shoppers who spent between 60 and 70 dollars stand apart from the other 38."

Four differences separate them:

• The second answer attaches a number and a unit to center and to spread. The first names the measures and stops.
• The second says who was measured and what the variable is. The first could be about anything.
• The second identifies the unusual features specifically: a gap in a stated interval, and 2 named high values. "A few outliers" locates nothing.
• The second states the shape and then supports it by pointing at the long right tail.

Naming a measure is not reporting it

"The center is the median" names a statistic and stops. A reader still does not know whether a typical shopper spent 3 dollars or 300 dollars. The same problem sinks "the spread is the IQR" and "the shape is the shape of the histogram". Every feature needs a value attached to it.

Two weaker versions also fall short:

• A value with no units. "The median is 15" leaves a grader choosing between dollars, minutes, and shoppers.
• A value with no context. "The median is 15 dollars" is better, but "the median amount spent by these 40 shoppers is about 15 dollars" is the version that scores.

Numbers read off a histogram are approximate, and that is fine. Write "about 15 dollars", or say the median falls in the 10 to 20 dollar bin. A defensible estimate beats a precise-looking number you could not have known from the display.

Which center and spread pair to report

Pick the pair that matches the shape you just named.

• Roughly symmetric with no outliers: report the mean $\bar{x}$ (read "x-bar", the sum of the values divided by how many there are) and the sample standard deviation $s$ (a typical distance of a value from the mean).
• Skewed, or outliers present: report the median and the interquartile range $\text{IQR} = Q_3 - Q_1$, where $Q_1$ (the first quartile) and $Q_3$ (the third quartile) bound the middle 50% of the data.

The reason is resistance. The AP course calls the median and IQR resistant, because outliers barely move them, and calls the mean, range, and standard deviation nonresistant. A single large value drags the mean upward and inflates the standard deviation while the median holds nearly still.

Reporting both pairs is allowed, but the pair you lean on should match the shape you just named. Leaning on the mean for a badly skewed distribution invites a follow-up about the outlier you did not mention, while the median and IQR describe the bulk of the data without that argument.

Unusual features: outliers, gaps, and clusters

The AP course defines these three precisely. An outlier is a value that is unusually small or large relative to the rest of the data. A gap is a region inside the distribution where no values were observed. A cluster is a concentration of values, usually set off from the others by a gap.

Modality belongs in the shape sentence. A distribution with one main peak is unimodal, one with two prominent peaks is bimodal, and one where every bar is about the same height with no prominent peak is approximately uniform. A bimodal shape often means two different groups got pooled into one graph, which is worth a sentence of its own.

When you have the raw data instead of a picture, you can back up an outlier claim with the 1.5 IQR rule rather than calling it by eye. From a histogram alone, "an apparent outlier" or "a value that stands apart from the rest" is the honest phrasing.

Where the points actually get lost

• Skipping unusual features. This is the single most common omission, and it costs the same as skipping center.
• Reversing the skew. The tail names the skew. A long right tail toward the large values is skewed right, no matter where the peak sits. Skewed left vs skewed right settles it.
• Describing the graph instead of the data. "The bars go down as you move right" is not a shape claim. "The distribution is skewed to the right" is.
• Dropping the units. Units are part of the context, and a number without them is incomplete.
• Reporting the mean for a badly skewed distribution and then never mentioning that an outlier pulled it.
• Answering a comparison question with one description. If two groups are shown, you owe a comparison, which is a different task. See how to compare two distributions.

Where this sits in the AP course

Describing distributions is topic 1.6 in Unit 1 of the Fall 2026 AP Statistics course, supported by topic 1.7 (summary statistics) and topic 1.8 (boxplots). Unit 1, Exploring One-Variable Data and Collecting Data, carries 20 to 30% of the multiple-choice section, and the skill being scored is 4.A, describing and comparing representations of data and summary statistics.

This shows up on free-response questions as often as on multiple choice, so practice writing the four sentences out. Work a set at describing distributions practice, or drag points and watch the shape change in the descriptive statistics sandbox. The official course description is at AP Central.