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. This concept is commonly used in statistics and probability to analyze the individual characteristics of a variable and its relationship to the overall data set.

One example of marginal distribution is the analysis of income levels within a population. In this case, the variable of interest is the income of individuals, and the marginal distribution would show 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.

Another example of marginal distribution is the analysis of exam scores within a classroom. In this case, the variable of interest is the exam score of each student, and the marginal distribution would show 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.

Overall, marginal distribution is a useful tool for understanding the individual characteristics of a variable within a data set and its relationship to the overall data. This information can provide valuable insight for decision making and identifying potential areas for improvement.