Final answer:
Variables are classified as discrete if the data can be counted, and as continuous if the data can be measured on a continuous scale. A variable representing the number of books is discrete; if it represents weight, it is continuous. Outliers can be identified in continuous data using specific formulas related to the interquartile range.
Step-by-step explanation:
The definition of whether a variable is discrete or contiguous (continuous) depends on whether the data can be counted in whole numbers or measured on a continuous scale. For instance, if variable X represents the number of books in a backpack, it is a discrete variable because you can count the number of books. However, if variable Y represents the weight of a book, it is a continuous variable because weight is measured and can take on any value within a range.
Data types such as the number of times per week are discrete because they involve counting occurrences. Duration or amount of time, on the other hand, are examples of continuous data since time can be measured in increasingly smaller units, such as seconds or milliseconds. When describing a histogram based on continuous data, one might note its shape—whether it is symmetrical, skewed, or uniform—and identify any potential outliers by calculating if they fall significantly outside the range of the majority of the data points. When analyzing survey questions, it is also important to determine the data type. For example, the number of books purchased in a semester is discrete, while the total amount spent on those books would be continuous.