Which of the following best describes the difference between relative frequency $f=\frac{n}{N}$ and cumulative frequency $F$ in probability?

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

Answer: (D)

Verified step by step guidance

1. Understand that relative frequency refers to the proportion of times a specific event occurs compared 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. Recognize that cumulative frequency is the running total of frequencies up to a certain point in the dataset. It sums the frequencies of all events or values less than or equal to a particular value.
3. Note that relative frequency focuses on individual event proportions, while cumulative frequency accumulates counts progressively through the dataset.
4. Compare the two concepts: relative frequency gives insight into the likelihood of a single event, whereas cumulative frequency helps understand the distribution and how frequencies build up across values.
5. Conclude that the correct description distinguishes relative frequency as a proportion for a single event and cumulative frequency as the sum of frequencies up to a certain value, which aligns with the last option provided.