Question

state whether the data described below are discrete or continuous, and explain why.
the numbers of typos in different students essays

choose the correct answer below.
a. the data are continuous because the data can take on any value in an interval.
b. the data are discrete because the data can only take on specific values.
c. the data are discrete 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 typos in students' essays) is discrete or continuous, we recall the definitions: Discrete data consists of distinct, separate values (like counts, which can't be a fraction, e.g., 0, 1, 2 typos), while continuous data can take any value in an interval (e.g., height, weight with decimals). The number of typos must be a non - negative integer (specific values, not a fraction or any value in an interval). So we analyze each option:

• Option A: Says data is continuous (can take any value in an interval), but number of typos can't be any value in an interval (e.g., you can't have 1.5 typos), so A is wrong.
• Option B: Says data is discrete (can only take on specific values). The number of typos is a count, so it can only be 0, 1, 2, … (specific values), so B is correct.
• Option C: Says discrete data can take any value in an interval, but by definition discrete data can't take any value in an interval, so C is wrong.
• Option D: Says continuous data can only take specific values, but continuous data is defined as taking any value in an interval, so D is wrong.

Answer:

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