In Exercises 13–20, determine whether the data are from a discrete or continuous data set.
Fraud Detection While monitoring Internet traffic in order to detect fraudulent activity, a researcher records the interarrival times (sec) between incoming Internet queries.

Verified step by step guidance

1. Understand the difference between discrete and continuous data: Discrete data can take on only specific, distinct values (often counts), while continuous data can take on any value within a range (often measurements).
2. Identify the variable in question: In this problem, the variable is the 'interarrival times (sec) between incoming Internet queries.'
3. Consider the nature of the variable: Time is typically measured and can take on any value within a range, including fractions of a second.
4. Determine if the variable can take on an infinite number of values within a given range: Since time can be measured to any level of precision (e.g., 1.5 seconds, 1.75 seconds, etc.), it is continuous.
5. Conclude that the data set is continuous because the interarrival times can be any real number within a range, not just distinct, separate values.

Key Concepts

Discrete Data

Discrete data consists of distinct, separate values that can be counted. Examples include the number of students in a class or the number of cars in a parking lot. Discrete data typically arises from counting processes and cannot take on fractional values, making it suitable for scenarios where only whole numbers are meaningful.

Continuous Data

Continuous data, in contrast, can take on any value within a given range and is often measured rather than counted. This type of data includes measurements such as height, weight, or time, where values can be infinitely divided into smaller increments. Continuous data is represented on a continuum and can include fractions or decimals.

Interarrival Times

Interarrival times refer to the time intervals between consecutive events, such as the arrival of Internet queries in this context. These times are typically measured in units like seconds and can take on any positive value, making them a prime example of continuous data. Understanding interarrival times is crucial in fields like queuing theory and network traffic analysis.