Marginal Distribution

TL;DR

Describes how values of one variable are distributed within a data set.
Often visualized with simple plots (e.g., histograms or line graphs) showing counts or frequencies.
Helps reveal patterns, gaps, or disparities in that single variable relative to the overall data.

Definition

Marginal distribution refers to the distribution of a single variable within a data set, as opposed to the joint distribution of two or more variables.

Explanation

In statistics and probability, marginal distribution is used to analyze the individual characteristics of one variable and its relationship to the overall data set. It isolates the behavior of that variable without conditioning on or simultaneously considering other variables.

Examples

Income levels within a population

The variable of interest is the income of individuals. The marginal distribution shows the distribution of income levels within the population. This could be represented through a histogram, with the x-axis representing income levels and the y-axis representing the number of individuals within each income level. This analysis can provide insight into the distribution of income within the population and identify any potential gaps or disparities.

Exam scores within a classroom

The variable of interest is the exam score of each student. The marginal distribution shows the distribution of scores within the class. This could be represented through a line graph, with the x-axis representing exam scores and the y-axis representing the number of students who received each score. This analysis can provide insight into the overall performance of the class and identify any areas where the majority of students may be struggling.

Use cases

Informing decision making and identifying potential areas for improvement by examining a single variable’s distribution within a data set.

Joint distribution