Sure, let me guide you through the solution step-by-step.
1. Identify the given data:
- We have a frequency table that shows the preferences of students for a 15-minute break.
- The table provides data for 10th, 11th, and 12th graders as well as the total number of students surveyed.
```
| Grade | Morning | Afternoon | Total |
|-------|---------|-----------|-------|
| 10th | 21 | 17 | 38 |
| 11th | 16 | 25 | 41 |
| 12th | 19 | 20 | 39 |
| Total | 56 | 62 | 118 |
```
2. Locate the specific data for 11th graders who prefer the afternoon break:
- From the table, the number of 11th graders who prefer the afternoon break is 25.
3. Calculate the total number of students surveyed:
- The total number of students surveyed is given as 118.
4. Calculate the joint relative frequency:
- The joint relative frequency is calculated by dividing the number of 11th graders who prefer the afternoon break by the total number of students surveyed.
- The formula is:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{\text{Number of 11th graders who prefer the afternoon break}}{\text{Total number of students}} \right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{25}{118} \right) \times 100
\][/tex]
[tex]\[
\text{Joint Relative Frequency} \approx 21.186 \%
\][/tex]
5. Round the result to the nearest percent:
- Rounding 21.186 to the nearest percent gives 21%.
6. Conclusion:
- The joint relative frequency for 11th graders who want the break in the afternoon, rounded to the nearest percent, is [tex]\( 21\% \)[/tex].
So, the correct answer is [tex]\( 21\% \)[/tex].
