What does a two-way frequency distribution typically display?

A two-way frequency distribution is a statistical tool that provides a way to display the joint distribution of values for two categorical (often binary or discrete) variables. This type of distribution organizes data into a matrix format, where one variable is represented in the rows and the other variable is represented in the columns. Each cell in the matrix counts the frequency of observations that fall into the corresponding categories for both variables.

For example, if one variable indicates whether individuals are male or female, and another variable indicates whether they have a driver's license, the two-way frequency distribution would show the counts of males with driver's licenses, females with driver's licenses, males without driver's licenses, and females without driver's licenses. This helps to visualize and analyze the relationship and dependencies between the two categorical variables.

In contrast, other options present different statistical scenarios. The correlation between two continuous variables involves calculating correlation coefficients rather than creating a frequency distribution. The average of two datasets pertains to summarizing data with measures of central tendency, not joint frequency distributions. Lastly, while examining the relationship between one continuous variable and one categorical variable is crucial in statistics, this scenario usually requires different analytical methods, such as regression analysis, rather than a two-way frequency distribution.