Let's solve the problem step-by-step to find the joint relative frequency of students who like running and swimming.
1. Identify the given numbers in the two-way frequency table:
- The number of students who enjoy swimming and like running is [tex]\( 28 \)[/tex].
- The total number of students surveyed is [tex]\( 200 \)[/tex].
2. Definition:
- The joint relative frequency is a measure of how often two characteristics occur together relative to the total number of observations. It is calculated using the formula:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{\text{Number of students who enjoy swimming and like running}}{\text{Total number of students}} \right) \times 100
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Joint Relative Frequency} = \left( \frac{28}{200} \right) \times 100
\][/tex]
4. Perform the division:
[tex]\[
\frac{28}{200} = 0.14
\][/tex]
5. Convert the decimal to a percentage:
[tex]\[
0.14 \times 100 = 14\%
\][/tex]
Therefore, the joint relative frequency of students who like running and swimming is [tex]\( 14\% \)[/tex].
