Multiple Choice
Which of the following frequency tables represents a skewed data set?
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2. Describing Data with Tables and Graphs
Frequency Distributions
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Which of the following best describes the difference between and in a frequency distribution?
A
shows the proportion of observations in each class, while shows the total number of observations up to and including each class.
B
and are always equal for every class in a distribution.
C
is the total number of observations, while is the proportion in each class.
D
is used only for qualitative data, while is used only for quantitative data.
Verified step by step guidance1
Step 1: Understand what relative frequency means. Relative frequency is the proportion or fraction 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, expressed as \(\text{Relative Frequency} = \frac{\text{Frequency of class}}{\text{Total number of observations}}\).
Step 2: Understand what cumulative frequency means. Cumulative frequency is the running total of frequencies up to and including a particular class. It shows how many observations fall within or below that class. It is calculated by adding the frequency of the current class to the cumulative frequency of the previous class.
Step 3: Compare the two concepts. Relative frequency focuses on the proportion of observations in each individual class, while cumulative frequency focuses on the total count of observations up to a certain class, accumulating as you move through the classes.
Step 4: Evaluate the answer choices based on these definitions. The correct description should reflect that relative frequency is a proportion for each class, and cumulative frequency is a total count up to that class.
Step 5: Conclude that the best 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.'
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