Question

state whether the data described below are discrete or continuous, and explain why. the number of donations a charity receives each month. choose the correct answer below. a. the data are discrete because the data can take on any value in an interval. b. the data are continuous because the data can take on any value in an interval. c. the data are discrete because the data can only take on specific values. d. the data are continuous because the data can only take on specific values.

Explanation:

To determine if the data (number of donations a charity receives each month) is discrete or continuous, we recall the definitions:

• Discrete data consists of distinct, separate values (like counts of items, which must be whole numbers here as you can't have a fraction of a donation).
• Continuous data can take any value within an interval (e.g., measurements like height, weight).

The number of donations must be a non - negative integer (0, 1, 2, ...). It can only take on specific values (whole numbers) and not any value in an interval. So the data is discrete.

Now let's analyze the options:

• Option A: Says discrete data can take any value in an interval, which is wrong. Discrete data has distinct values.
• Option B: Claims the data is continuous, but the number of donations can't be a non - whole number, so it's not continuous.
• Option C: Correctly states the data is discrete because it can only take on specific values (whole numbers for the count of donations).
• Option D: Says continuous data can only take specific values, which is a wrong definition of continuous data.

Answer:

C. The data are discrete because the data can only take on specific values.