Question

state whether the data described below are discrete or continuous, and explain why. the numbers of countries in the world in different years choose the correct answer below. a. the data are discrete because the data can only take on specific values. b. the data are discrete because the data can take on any value in an interval. c. the data are continuous because the data can take on any value in an interval. d. the data are continuous because the data can only take on specific values.

Explanation:

To determine if the data (numbers of countries in different years) is discrete or continuous, we recall:

• Discrete data can only take specific, distinct values (like counts of objects, which must be whole numbers here as you can't have a fraction of a country).
• Continuous data can take any value in an interval (e.g., measurements like height, weight).

The number of countries is a count, so it can only be specific whole numbers (e.g., 195 countries, not 195.5). So the data is discrete because it takes specific values. Option A matches this reasoning, while B misdefines discrete, C and D misclassify as continuous (with D also misdefining continuous).

Answer:

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