The table below shows the results of a survey about vacation destinations and the length of those vacations.
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Which of the following includes the correct relative frequency and conclusion based on the table?
A
The relative frequency for traveling in state for longer than a week is 17%. This could be low because people want to spend more time if they have traveled farther.
B
The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther.
C
The relative frequency for traveling in state for longer than a week is 30%. This could be low because people want to spend more time if they have traveled farther.
D
The relative frequency for traveling out of state for longer than a week is 83%. This could be high because people want to spend more time if they have traveled farther.
B. The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther.
The correct option is B.
The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther.
To determine the correct relative frequency and conclusion, we need to calculate the percentages based on the table provided.
Looking at the table, we can see that there are a total of 120 responses in the survey. To calculate the relative frequencies, we need to divide the number of responses for each category by the total number of responses (120).
For traveling in-state for longer than a week, we have 15 responses. So the relative frequency for this category is calculated as (15/120) * 100 = 12.5%.
For traveling out of state for longer than a week, we have 45 responses. So the relative frequency for this category is calculated as (45/120) * 100 = 37.5%.
Now, let's evaluate the conclusions based on these relative frequencies:
Option A states that the relative frequency for traveling in-state for longer than a week is 17% and people might want to spend more time if they have traveled farther. However, the correct relative frequency for this category is 12.5%, and the conclusion doesn't align with the data. Therefore, option A is incorrect.
Option B states that the relative frequency for traveling out of state for longer than a week is 48% and people might want to spend more time if they have traveled farther. The correct relative frequency for this category is 37.5%, and the conclusion aligns with the data. Therefore, option B seems to be the correct answer.
Option C states that the relative frequency for traveling in-state for longer than a week is 30% and people might want to spend more time if they have traveled farther. The correct relative frequency for this category is 12.5%, and the conclusion doesn't align with the data. Therefore, option C is incorrect.
Option D states that the relative frequency for traveling out of state for longer than a week is 83% and people might want to spend more time if they have traveled farther. The correct relative frequency for this category is 37.5%, and the conclusion aligns with the data. Therefore, option D is incorrect.
Based on the calculations, the correct answer should be option B: "The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther."