Which of the following best describes the difference between $\mathrm{relative} \mathrm{frequency}$ and $\mathrm{cumulative} \mathrm{frequency}$ in probability?

• A. $\mathrm{Relative} \mathrm{frequency}$ is the proportion of times an event occurs out of the total number of trials, while $\mathrm{cumulative} \mathrm{frequency}$ is the sum of frequencies for all values up to and including a certain value.
• B. $\mathrm{Relative} \mathrm{frequency}$ is the total number of occurrences of all events, while $\mathrm{cumulative} \mathrm{frequency}$ is the frequency of a single event.
• C. $\mathrm{Relative} \mathrm{frequency}$ and $\mathrm{cumulative} \mathrm{frequency}$ are two terms for the same concept in probability.
• D. $\mathrm{Relative} \mathrm{frequency}$ is always greater than $\mathrm{cumulative} \mathrm{frequency}$ for any dataset.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of relative frequency. Relative frequency is calculated as the ratio of the number of times a specific event occurs to the total number of trials or observations. Mathematically, it is expressed as \(\text{Relative Frequency} = \frac{\text{Frequency of event}}{\text{Total number of trials}}\).
2. Step 2: Understand the concept of cumulative frequency. Cumulative frequency is the running total of frequencies up to and including a particular value or category. It sums all frequencies from the first category up to the current one.
3. Step 3: Recognize that relative frequency focuses on the proportion of a single event relative to the whole dataset, while cumulative frequency aggregates frequencies across multiple events or categories up to a point.
4. Step 4: Compare the two definitions to identify the key difference: relative frequency measures the proportion for one event, whereas cumulative frequency measures the total count up to a certain value.
5. Step 5: Use this understanding to evaluate the given answer choices and select the one that correctly describes relative frequency as a proportion of total trials and cumulative frequency as the sum of frequencies up to a certain value.