Final answer:
A parameter is a numerical characteristic of an entire population, whereas a statistic represents a sample. In the example given, the professor calculating a class average is determining a parameter. The 50 percent of high school seniors planning to attend a four-year college from the survey is a statistic.
Step-by-step explanation:
The question 'Which of the following describes a parameter?' pertains to the concept of parameters in the context of statistics, a field within mathematics. A parameter is a numerical characteristic of a whole population, and it differs from a statistic, which is a characteristic of a sample. When you are working with data from the entire population, you are dealing with a parameter. For example, if a professor calculates the average exam score for her class using the scores of all students, she is calculating a parameter because it includes the entire population of her class. On the other hand, a statistic is calculated using sample data, representing only a subset of the population.
If we refer to the U.S. federal government's survey of high school seniors with the question concerning their plans for future education and employment, the 50 percent who answered that they are planning to attend a four-year college or university represents a statistic because it is derived from a sample of the population, rather than the entire population.
When discussing variables, we acknowledge these characteristics can be either numerical (quantitative) or categorical. Numerical variables can have mathematical operations performed on them, such as calculating an average. Categorical variables, such as political party affiliation, are qualitative and do not lend themselves to mathematical operations like obtaining an average.