Final answer:
A variable is any event or quality that can take on different values, including numerical and categorical types, and it is fundamental in data analysis and mathematical equations.
Step-by-step explanation:
Any event or quality that can assume more than one value is called a variable. A variable is a characteristic, number, or quantity that can be measured or quantified. Variables fall into different categories, such as numerical and categorical. Numerical variables are values with equal units like weight or time, and they can be either discrete or continuous.
Discrete numerical variables are the result of counting, such as the number of books on a shelf, while continuous numerical variables result from measuring, such as the weight of luggage. On the other hand, categorical variables such as political affiliation, put individuals into categories like Republican, Democrat, and Independent where it would make no sense to perform mathematical operations like calculating an average. Variables are fundamental in data analysis, and in the context of equations and functions, like the equation of a line, variables like x and y represent points on a graph.