Which of the following best describes the difference between $relative frequency$ and $cumulative frequency$ in a frequency distribution?

• A. $Relative frequency$ is the total number of observations, while $cumulative frequency$ is the proportion of observations in each class.
• B. $Relative frequency$ shows the proportion of observations in each class, while $cumulative frequency$ shows the total number of observations up to and including each class.
• C. $Relative frequency$ is used only for qualitative data, while $cumulative frequency$ is used only for quantitative data.
• D. $Relative frequency$ and $cumulative frequency$ both represent the total number of observations in all classes.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of relative frequency. Relative frequency represents the proportion or percentage of the total number of observations that fall within a particular class or category. It is calculated by dividing the frequency of a class by the total number of observations.
2. Step 2: Understand the concept of cumulative frequency. Cumulative frequency is the running total of frequencies up to and including a particular class. It shows how many observations fall within or below a certain class boundary.
3. Step 3: Compare the two concepts. Relative frequency focuses on the proportion within each individual class, while cumulative frequency accumulates counts from the first class up to the current class.
4. Step 4: Recognize that relative frequency is expressed as a proportion or percentage, whereas cumulative frequency is expressed as a count or total number of observations.
5. Step 5: Conclude that the correct description is: Relative frequency shows the proportion of observations in each class, while cumulative frequency shows the total number of observations up to and including each class.