Which of the following statements is true regarding relative frequency distributions?

• A. The sum of all relative frequencies in a distribution is always greater than $1$.
• B. Relative frequency distributions cannot be used for categorical data.
• C. Relative frequencies are always expressed as whole numbers only.
• D. The sum of all relative frequencies in a distribution is always equal to $1$.

Answer: (D)

Verified step by step guidance

1. Understand that a relative frequency distribution shows the proportion of the total number of data points that fall into each category or class.
2. Recall that relative frequency for each category is calculated by dividing the frequency of that category by the total number of observations, i.e., \(\text{Relative Frequency} = \frac{\text{Frequency of category}}{\text{Total frequency}}\).
3. Recognize that since all categories together account for the entire dataset, the sum of all relative frequencies must represent the whole, which means the sum should be exactly 1, or 100% when expressed as a percentage.
4. Note that relative frequency distributions can be used for both categorical and numerical data, so the statement that they cannot be used for categorical data is false.
5. Understand that relative frequencies are typically expressed as decimals or percentages, not necessarily as whole numbers, so the statement about them always being whole numbers is incorrect.