Overview
This lecture explains how to identify the number of peaks ("mounds") in a distribution, defines various types of distributions based on their shape, and introduces key statistical terms such as unimodal, bimodal, multimodal, uniform, and normal distributions, as well as the concept of outliers.
Identifying Mounds in Distributions
- A "mound" refers to a peak in the outline of a histogram, not just a single bar.
- The number of mounds is determined by tracing the outer outline of the histogram and counting the peaks.
- Most graphs in elementary statistics are unimodal (one mound).
Types of Distributions by Mounds
- Unimodal distributions have one distinct peak or mound.
- Bimodal distributions have two distinct peaks, often due to combining two different groups (e.g., male and female heights).
- Multimodal distributions have three or more peaks.
Causes of Multiple Mounds
- Multiple mounds typically occur when data from different groups are combined in a single graph.
- Each group on its own generally shows a unimodal distribution, but combined they can result in bimodal or multimodal shapes.
Other Distribution Shapes
- Uniform distributions have the same frequency for all observations, resulting in no mounds and a horizontal line.
- Most real-world data will not be uniform, but the term means "same frequency" for all values.
Symmetry and Normal Distributions
- Shape of data is described by symmetry (symmetric or skewed) and the number of mounds.
- A "normal" distribution is both symmetric and unimodal.
- The normal distribution is a central concept in statistics and will be covered extensively in future chapters.
Outliers
- Outliers are extremely large or small values that don’t fit the rest of the data.
- Currently, outliers are identified visually ("eyeballing"), but a mathematical method will be taught in Section 3.5.
Key Terms & Definitions
- Mound — A peak in the outline of a histogram.
- Unimodal — A graph with one peak.
- Bimodal — A graph with two distinct peaks.
- Multimodal — A graph with three or more distinct peaks.
- Uniform Distribution — All frequencies are the same; no mounds.
- Normal Distribution — A distribution that is symmetric and unimodal.
- Outlier — A data value much larger or smaller than the rest.
Action Items / Next Steps
- Be prepared to define and identify unimodal, bimodal, multimodal, uniform, and normal distributions.
- Watch for the introduction of a mathematical method for outlier identification in Section 3.5.