In Exercises 13–20, determine whether the data are from a discrete or continuous data set.
Students Your statistics professor records the number of students who pass each of her courses.

Verified step by step guidance

1. Understand the definitions: Discrete data consists of countable values, often integers, while continuous data can take any value within a range, often involving measurements.
2. Identify the variable in question: The problem mentions the 'number of students who pass each course.'
3. Consider the nature of the variable: The number of students is a countable quantity, meaning it can only take integer values (e.g., 1, 2, 3, etc.).
4. Determine the type of data: Since the number of students is countable and can only be whole numbers, it is a discrete data set.
5. Conclude with reasoning: Discrete data is characterized by distinct, separate values, which aligns with counting students. Continuous data would involve measurements that could be infinitely precise, such as time or temperature.

Key Concepts

Discrete Data

Discrete data refers to countable values that can only take specific, distinct values. Examples include the number of students in a class or the number of cars in a parking lot. In this context, since the professor records the number of students passing her courses, the data is discrete because it consists of whole numbers that cannot be subdivided.

Continuous Data

Continuous data, in contrast, can take any value within a given range and can be measured rather than counted. Examples include height, weight, or temperature, where values can be infinitely divided. Understanding the difference between discrete and continuous data is crucial for selecting appropriate statistical methods for analysis.

Data Sets

A data set is a collection of related data points that can be analyzed to extract meaningful information. Data sets can be classified as either discrete or continuous based on the nature of the data they contain. Recognizing the type of data set is essential for applying the correct statistical techniques and interpreting results accurately.