Final answer:
Categorical variables classify data into groups or categories and are qualitative, while quantitative variables are numerical and divisible into discrete data (from counting) or continuous data (from measuring). Examples include political party affiliation for categorical, and number of classes (discrete), or distance to a store (continuous) for quantitative.
Step-by-step explanation:
Categorical variables are types of data that place individuals or items into groups or categories. An example of a categorical variable is a person's political party affiliation. It is qualitative and describes an attribute through labels or names, such as Republican, Democrat, or Independent. These types of variables do not lend themselves to mathematical operations like finding averages.
Quantitative variables, on the other hand, can be measured numerically and are divided into two subgroups: discrete and continuous. Quantitative discrete data result from counting, like the number of classes a student takes per year. Quantitative continuous data result from measuring, such as the distance to the nearest grocery store, and can take an infinite number of values within a range.
Identifying the type of data is crucial for analysis. For instance, 'the number of times per week' a person does an activity is quantitative discrete data, while 'the distance from your home to the nearest grocery store' is quantitative continuous data. Categories like 'the type of car you drive' represent categorical data.