Final answer:
Categorical variables categorize individuals or objects, while continuous variables measure data that can assume any value within a range. Discrete variables, a subset of quantitative data, represent countable quantities and their probabilities sum to one.
Step-by-step explanation:
The difference between a categorical variable and a continuous variable lies in the type of data they represent and how they are used in statistics.
A categorical variable is one that places an individual or an object into a category. Examples of categorical variables include political affiliation, type of car, and type of calculator. Categorical variables are used for data that can be divided into groups that are qualitatively different from each other.
In contrast, a continuous variable is associated with numerical data that can take on any value within a given range. The values of continuous variables are obtained through measurements, not by counting, and can be any number within the possible range, including fractions and decimals.