A categorical variable is a type of variable in statistics that represents categories or groups. Unlike numerical variables that represent measurable quantities, categorical variables are used to label or categorize data into distinct groups or classes. Categorical variables can be further divided into two main types: nominal and ordinal.

Nominal Categorical Variable:

• Nominal variables represent categories with no inherent order or ranking.
• Examples include gender (male, female), colors (red, blue, green), or types of fruits (apple, orange, banana).
• Nominal variables are often used to classify or group observations without implying any specific order.

Ordinal Categorical Variable:

• Ordinal variables represent categories with a meaningful order or ranking.
• While the categories have an order, the intervals between them may not be uniform or measurable.
• Examples include education levels (high school, college, graduate), customer satisfaction ratings (poor, fair, good, excellent), or socioeconomic status (low, middle, high).
• Ordinal variables provide information about the relative position or ranking of the categories, but the differences between them may not be precisely defined.

Categorical variables are often represented using labels or names, and statistical analyses involving categorical variables may include techniques like contingency tables, chi-square tests, or logistic regression, depending on the nature of the data and research questions.