Final answer:
A two-way table, or contingency table, is used to display bivariate descriptive statistics, which consists of data for two variables. It facilitates the calculation of probabilities as well as marginal and conditional distributions. These contingency tables are essential for analyzing the relationship between two categorical variables.
Step-by-step explanation:
The two-way table, also known as a contingency table, showcases bivariate descriptive statistics. Bivariate data consists of two variables and helps in calculating different statistical measures, including marginal and conditional distributions.
These types of tables are particularly useful for representing the relationship between two categorical variables and for facilitating the calculation of probabilities.
For example, accounting for the favorite sports of men and women, a two-way table would display the count of individuals that prefer each sport across both genders. The marginal frequencies, which are found in the margins of the table, represent the total count for one of the variables independent of the other. When these marginal frequencies are expressed as fractions or decimals, they are termed as marginal distributions.
In practice, statisticians may also use tables such as histograms, stem-and-leaf plots (stemplots), and box plots for univariate data, while two-way tables are specifically utilized for bivariate data.