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Describing
Distribution Shape

Learn to identify and describe the shape, clusters, gaps, and outliers of data distributions and explain what they mean in real-world context.

AP Statistics

What Is a Distribution?

A distribution shows how data values are spread out along a number line. When you collect data: test scores, heights, shoe sizes: you can display them in a dot plot, histogram, or bar graph to see the overall pattern.

60 70 80 90 100 Test Scores (dot plot)

Four Features of Distribution Shape

Shape
Is the data symmetric, skewed left, or skewed right?
Clusters
Where do data points group together?
Gaps
Are there empty spaces with no data?
Outliers
Are any values far away from the rest?

Understanding Shape

Symmetric Mirror image Skewed Right Tail stretches right Skewed Left Tail stretches left tail tail

Clusters and Gaps

1 2 3 4 5 6 7 8 9 10 Hours of Sleep Gap Cluster 1 Cluster 2
Cluster
A group of data points that are close together. Here, most students sleep 5-7 hours.
Gap
An area with no data values. No students reported 8 hours of sleep.

Spotting Outliers

50 60 70 80 90 100 Quiz Scores Outlier!

In context: This student may have been absent during the review or misunderstood the material. Outliers always deserve an explanation!

The Four-Feature Rule

1
Shape: Is the distribution symmetric, skewed left, or skewed right?
2
Clusters: Where do values concentrate? What does that group represent?
3
Gaps: Are there missing ranges? Why might those values be absent?
4
Outliers: Any extreme values? What could explain them?

Symmetric vs Skewed

Symmetric Skewed
Shape Both sides are mirror images One tail is longer than the other
Mean vs Median Roughly equal Mean pulled toward the tail
Example Heights of students in a class Household income in a city
Best Center Mean works well Median is more reliable

How to Describe a Distribution

1
Look at the overall shape. Is it symmetric, skewed left, or skewed right? Does it have one peak (unimodal) or two (bimodal)?
2
Identify clusters. Find where data points group together and note the range of those groups.
3
Spot any gaps. Look for empty stretches on the number line where no data falls.
4
Check for outliers. Are any values far from the main group? Circle them.
5
Explain in context. Use the actual variable name (e.g., "test scores") and give possible real-world reasons.

Example 1: Daily Steps

Daily Step Counts (thousands) 2 4 6 8 10 12 14 16 tail

Example 2: Class Heights

Student Heights (inches) 56 60 64 68 72 76 line of symmetry

Example 3: Movie Ratings

Movie Ratings (out of 10) 1 2 3 4 5 6 7 8 9 Gap "Hated it" "Loved it"

Why Context Matters

Numbers alone do not tell the full story. Explaining what the data means in real life is the most important part of describing a distribution.

Without Context
"The distribution is skewed right with a cluster at 4-8 and an outlier at 22."
With Context
"Most students read 4-8 books this year, but one student read 22, possibly because they are in a book club."

Common Mistakes

✕ Naming the Peak, Not the Tail
Saying "skewed left" when the peak is on the left. Remember: the tail names the direction.
✕ Forgetting Context
Describing only numbers without explaining what they mean in the real situation.
✕ Calling Every Extreme an Outlier
The highest or lowest value is not always an outlier. It must be separated from the group by a gap.

Summary of Key Terms

Feature What to Look For Example Phrase
Shape Symmetric, skewed left/right, bimodal "The distribution is skewed right."
Cluster Where data groups together "Most values cluster between 60 and 80."
Gap Empty spaces with no data "There is a gap from 40 to 55."
Outlier Values far from the rest "The value 98 is an outlier."
Context Real-world meaning "...because that student was absent."

Question 1 of 5

A histogram of household incomes in a city shows a tall peak on the left and a long tail stretching to the right. What is the shape of this distribution?

Question 2 of 5

In a dot plot of students' ages at a summer camp, there are dots at ages 8, 9, 10, and 11, but no dots at age 12, and then several dots at ages 13 and 14. What feature best describes the space at age 12?

Question 3 of 5

A data set of daily high temperatures in July shows values of 88, 90, 91, 89, 92, 90, 91, 88, 90, and 42. Which value is most likely an outlier?

Question 4 of 5

A distribution has two clear peaks: one around 20 minutes and another around 45 minutes. This distribution is best described as:

Question 5 of 5

Which of the following is the best description of a skewed-left distribution of exam scores?