To find the relative frequency that people who prefer island vacations also prefer swimming, we first need to determine the total number of people who prefer island vacations.
From the table, for those who prefer vacations at the island:
- Hiking: 12
- Swimming: The value is not provided, hence we'll denote it as
Xfor now.
To find the total number of people who prefer island vacations, we will sum the values (both hiking and swimming) for the island preference:
\[ \text{Total for Island} = \text{Hiking} + \text{Swimming} = 12 + X \]
Now we also need the total number of people who prefer swimming across all preferences (mountains, seaside, and island):
- For hiking: 45 + 12 + 12 = 69
- For swimming: 12 (mountains) + 53 (seaside) +
X(island) = 65 +X
Now, let's set up the proportion for those who prefer swimming compared to the total who prefer the island.
The relative frequency formula for swimming preferences among island vacationers is:
\[ \text{Relative Frequency} = \frac{\text{People who prefer swimming on island}}{\text{Total people who prefer island vacation}} \]
We can assume for the swimming on the island, it’s denoted as X. Thus we have:
\[ \text{Relative Frequency} = \frac{X}{12 + X} \]
If we are given that swimming on the island is represented as the unknown ??, we cannot calculate the exact relative frequency without its value.
Assuming ?? refers to the count for swimming on the island, let's denote it as 0 (if there was no data). Thus:
Relative Frequency = 0 / (12 + 0) = 0.
Thus, the final answer (if swimming = 0) is:
Relative Frequency percentage = 0%, rounded to the nearest tenth.
But if ?? were given an actual number, you would plug it into X to find a specific relative frequency.
If more information is available or if an assumption needs to be made on the unknown swimming value for the island, please specify!