In Exercises 13–20, determine whether the data are from a discrete or continuous data set.
Statistics Classes In each of her classes, a statistics professor records the number of students who earned a grade of A.

Verified step by step guidance

1. Understand the difference between discrete and continuous data: Discrete data can only take specific values (often integers), while continuous data can take any value within a range.
2. Identify the variable in the problem: The variable here is the 'number of students who earned a grade of A' in each class.
3. Consider the nature of the variable: The number of students is a countable quantity, meaning it can only be whole numbers (e.g., 0, 1, 2, 3, etc.).
4. Determine if the data can take any value within a range or only specific values: Since the number of students is countable and cannot be fractional, it is limited to specific integer values.
5. Conclude whether the data is discrete or continuous: Based on the analysis, the data is discrete because it consists of countable, specific values.

Key Concepts

Discrete Data

Discrete data refers to countable data points that can take on distinct, separate values. In the context of the question, the number of students earning a grade of A is a discrete data set because it involves counting individual students, resulting in whole numbers without fractions or decimals.

Continuous Data

Continuous data represents measurements that can take on any value within a given range, often involving fractions or decimals. Unlike discrete data, continuous data is not countable but measurable, such as height or temperature. Understanding this distinction helps in identifying the nature of the data set in the question.

Data Set Classification

Classifying data as discrete or continuous is crucial for selecting appropriate statistical methods. Discrete data often uses methods like frequency counts and probability distributions, while continuous data might involve measures like mean and standard deviation. Recognizing the type of data helps in applying the correct analytical techniques.