Question

determine whether the given value is from a discrete or continuous data set.
when a car is randomly selected, it is found to have an engine with 8 cylinders.

choose the correct answer below.

a. a continuous data set because there are infinitely many possible values and those values cannot be counted.

b. a continuous data set because there are infinitely many possible values and those values can be counted.

c. a discrete data set because there are a finite number of possible values.

d. the data set is neither continuous nor discrete.

Explanation:

To determine if the data is discrete or continuous, we recall the definitions: Discrete data consists of distinct, countable values (like the number of cylinders, which can only be whole numbers with a finite or countably infinite set of possible values). Continuous data can take any value in an interval (e.g., measurements like length or weight) and is uncountable in the sense of having infinitely many non - distinct, non - countable values. The number of cylinders in a car engine is a countable value (you can't have a fraction of a cylinder in a typical engine setup, and the possible number of cylinders is a finite set of whole numbers). Option A is wrong because continuous data can't be counted. Option B is wrong as continuous data can't be counted. Option D is wrong as the number of cylinders is either discrete or continuous, and here it's discrete. Option C correctly states that the number of cylinders is a discrete data set because the possible number of cylinders (e.g., 4, 6, 8, etc.) is a finite set of countable values.

Answer:

C. A discrete data set because there are a finite number of possible values.