The variable described, "the number of police officers in each of 10 communities", is discrete.

Reasoning:

A discrete variable is one that takes on a countable number of values. In this case:

• The number of police officers is a whole number (e.g., 0, 1, 2, ...).
• It cannot take fractional or decimal values, as you can't have "half" a police officer.
• Therefore, this variable is discrete.

A continuous variable, in contrast, would take on an infinite number of values within a range, such as height, weight, or time.

Do you need further explanation or examples of discrete and continuous variables?

Related Questions:

1. What are some other examples of discrete variables in real life?
2. How do you differentiate between discrete and continuous variables mathematically?
3. Can the number of people in a classroom also be considered a discrete variable? Why?
4. What is the significance of identifying a variable as discrete or continuous in statistics?
5. How would you graph a discrete variable compared to a continuous variable?

Tip: To identify if a variable is discrete, ask if it can be counted rather than measured. If the answer is "yes," the variable is likely discrete.