Overview
This lesson explains the shape of a distribution of a variable, focusing on how distributions are described and the different common shapes they can take.
Characteristics of a Distribution
- A distribution displays all possible values of a variable and the frequency of each value.
- Distributions can be shown as lists, tables, or graphs.
- Four main characteristics to examine: shape, outliers, center, and spread (sometimes called "SOCKS").
Common Shapes of Distributions
- Bell-shaped (normal) distributions are symmetric with one central peak.
- Symmetric distributions have left and right sides that are mirror images.
- Uniform distributions are symmetric and have equal frequencies across values.
- Skewed distributions are asymmetrical, with data clustering on one side and a long tail on the other.
- Left-skewed (negatively skewed) distributions have a tail to the left, data clusters to the right.
- Right-skewed (positively skewed) distributions have a tail to the right, data clusters to the left.
Unimodal and Bimodal Distributions
- Unimodal distributions have one clear peak or most frequent value.
- Bimodal distributions have two clear peaks or most frequent values.
- Skewed distributions can still be unimodal if they have one peak and a tail.
Key Terms & Definitions
- Distribution — The set of all possible values of a variable and their frequencies.
- Symmetric Distribution — A shape where left and right sides are mirror images.
- Bell-shaped/Normal Distribution — A symmetric distribution with a single central peak.
- Uniform Distribution — All values occur with approximately equal frequency (also symmetric).
- Skewed Distribution — A shape that is asymmetrical, with a tail on one side.
- Left-skewed/Negatively skewed — Tail to the left, data clusters to the right.
- Right-skewed/Positively skewed — Tail to the right, data clusters to the left.
- Unimodal Distribution — A distribution with one clear peak.
- Bimodal Distribution — A distribution with two clear peaks.
Action Items / Next Steps
- Review examples of each distribution shape in your textbook or class materials.