If it is impossible to divide the existing categories of a variable, then it is an example of a ____ variable.

If it is impossible to divide the existing categories of a variable, then it is an example of a ____ variable.

• A. Independent
• B. Dependent
• C. Discrete
• D. Continuous

Answer: (C)

The key idea here is the distinction between discrete and continuous variables based on whether you can subdivide the possible values into smaller, meaningful parts. If it’s impossible to divide the existing categories any further, the variable is discrete. That’s because discrete variables have separate, distinct values (often counts) that you can’t represent with intermediate values. For example, you can count people or items as whole numbers; you can’t have 2.5 people, so the values are inherently separate. Continuous variables, by contrast, can take on any value within a range and can be subdivided endlessly with increasing precision (like height, time, or temperature). So the scenario described—where the categories of the variable can’t be divided further—best fits a discrete variable.

The key idea here is the distinction between discrete and continuous variables based on whether you can subdivide the possible values into smaller, meaningful parts. If it’s impossible to divide the existing categories any further, the variable is discrete. That’s because discrete variables have separate, distinct values (often counts) that you can’t represent with intermediate values. For example, you can count people or items as whole numbers; you can’t have 2.5 people, so the values are inherently separate.

Continuous variables, by contrast, can take on any value within a range and can be subdivided endlessly with increasing precision (like height, time, or temperature). So the scenario described—where the categories of the variable can’t be divided further—best fits a discrete variable.