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 always greater than $\mathrm{cumulative} \mathrm{frequency}$ for any dataset.
• 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. $\mathrm{Relative} \mathrm{frequency}$ 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.
• D. $\mathrm{Relative} \mathrm{frequency}$ and $\mathrm{cumulative} \mathrm{frequency}$ are two terms for the same concept in probability.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definition of relative frequency. Relative frequency is the ratio of the number of times a specific event occurs to the total number of trials or observations. It is calculated as \(\text{Relative Frequency} = \frac{\text{Frequency of a specific event}}{\text{Total number of observations}}\).
2. Step 2: Understand the definition of cumulative frequency. Cumulative frequency is the running total of frequencies up to and including a certain value or category. It sums the frequencies of all events or values less than or equal to a particular point.
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 from the start of the dataset up to a certain event or value.
4. Step 4: Compare the two concepts: relative frequency gives insight into the likelihood of a single event, whereas cumulative frequency helps understand the accumulation or distribution of data up to a point.
5. Step 5: Conclude that the correct description is that relative frequency is the proportion of times an event occurs out of the total number of trials, while cumulative frequency is the sum of frequencies for all values up to and including a certain value.