Interpret and summarize distributions (center, spread, shape, outliers).
Describe a distribution by its center, spread, shape, and unusual values.
Core Idea
Describe a distribution by its center, spread, shape, and unusual values. Outliers can pull the mean more than the median, and skew tells you which side has the longer tail.
Understanding
Rule: A full summary of a distribution is not just one number. You should notice where the data cluster, how spread out they are, whether the shape is roughly symmetric or skewed, and whether any values sit far from the rest.
This matters because different summaries react differently to outliers. A large high value can pull the mean upward, while the median may stay closer to the middle of the main cluster. When a distribution is skewed, that shape helps explain why the mean and median may not match.
Step by Step
- Identify the center of the data.
- Notice the spread and whether any values are far from the rest.
- Use the outlier or skew to explain why the mean and median differ.
Misconceptions
- Calling a distribution symmetric when one extreme value pulls the mean away from the center.
- Using the mean as the only measure of center when the data are skewed.
- Treating any large number as an outlier without comparing it to the rest of the data.
Worked Example
The data set
Select an answer to see the explanation