Which of the following best describes what a frequency distribution lists?

• A. The $\mathrm{mean}$ and $\mathrm{standard\; deviation}$ of the data
• B. The $\sum$ of all data values
• C. Only the $\mathrm{highest}$ and $\mathrm{lowest}$ values in a data set
• D. All possible values of a variable and the number of times each value occurs

Answer: (D)

Verified step by step guidance

1. Understand that a frequency distribution is a way to organize data to show how often each value occurs in a data set.
2. Recognize that it lists all possible values of the variable being studied, not just summary statistics like the mean or standard deviation.
3. Know that for each value, the frequency distribution records the number of times that value appears, which helps in understanding the data's distribution.
4. Note that it does not focus on just the highest or lowest values, nor does it sum all data values; instead, it provides a count for each distinct value.
5. Therefore, the best description of a frequency distribution is that it lists all possible values of a variable and the number of times each value occurs.