Sure! Let's solve the problem step-by-step to find the joint relative frequency of students who like both running and swimming.
1. Understand the given data:
The two-way frequency table provides the following relevant information:
- The number of students who like both running and swimming is 28.
- The total number of students surveyed is 200.
2. Define joint relative frequency:
The joint relative frequency is found by dividing the number of students who like both activities by the total number of students surveyed. This gives us a fraction that represents the proportion of students who like both activities relative to the entire student population.
3. Calculate the joint relative frequency:
[tex]\[
\text{Joint relative frequency} = \frac{\text{Number of students who like both running and swimming}}{\text{Total number of students}}
\][/tex]
Substitute the given values:
[tex]\[
\text{Joint relative frequency} = \frac{28}{200}
\][/tex]
4. Simplify the fraction:
The calculation is:
[tex]\[
\frac{28}{200} = 0.14
\][/tex]
5. Convert the joint relative frequency to a percentage:
To express the joint relative frequency as a percentage, multiply by 100:
[tex]\[
0.14 \times 100 = 14\%
\][/tex]
6. Conclusion:
The joint relative frequency of students who like both running and swimming is \( 0.14 \) or \( 14\% \).
So the correct answer is [tex]\( 14\% \)[/tex].
