The residents of three towns were polled to find the percentage of residents who take a vacation in the summer or in the winter.
Vacations
| | Summer | Winter | Total |
| :----- | :----- | :----- | :---- |
| Town 1 | 567 | 87 | 654 |
| Town 2 | 345 | 102 | 447 |
| Town 3 | 143 | 158 | 301 |
| Total | 1,055 | 347 | 1,402 |
Which is the joint relative frequency of those in Town 2 who take a summer vacation? Round the answer to the nearest percent.
Answer (2)
The joint relative frequency of Town 2 residents who take a summer vacation is about 25%. This is calculated by dividing the number of vacationers by the total population and converting it to a percentage. The calculation gives us a value of 24.607% which rounds to 25%.
;
Find the number of residents in Town 2 who take a summer vacation: 345.
Find the total number of residents: 1402.
Calculate the joint relative frequency: 1402 345 ≈ 0.246 .
Round to the nearest percent: 25% .
Explanation
Understand the problem We are asked to find the joint relative frequency of those in Town 2 who take a summer vacation. This means we need to find the proportion of the total population that is represented by the residents of Town 2 who take a summer vacation.
Identify the relevant numbers From the table, we see that 345 residents of Town 2 take a summer vacation. The total number of residents across all towns is 1402.
Calculate the joint relative frequency To find the joint relative frequency, we divide the number of residents in Town 2 who take a summer vacation by the total number of residents: 1402 345
Convert to percentage and round Now, we need to calculate this fraction as a percentage and round to the nearest percent. 1402 345 ≈ 0.246077
To express this as a percentage, we multiply by 100: 0.246077 × 100 = 24.6077%
Rounding this to the nearest percent, we get 25%.
State the final answer Therefore, the joint relative frequency of those in Town 2 who take a summer vacation is approximately 25%.
Examples
Joint relative frequency is useful in market research. For example, a company might want to know the joint relative frequency of customers who are female and prefer a certain product. This helps them understand their customer base better and tailor their marketing strategies.
