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The two-way frequency table contains data about students' preferred exercise.

\begin{tabular}{|c|l|l|l|}
\hline
& Enjoys swimming & Enjoys cycling & Row totals \\
\hline
Likes running & 28 & 62 & 90 \\
\hline
Does not like running & 46 & 64 & 110 \\
\hline
Column totals & 74 & 126 & 200 \\
\hline
\end{tabular}

What is the joint relative frequency of students who like running and swimming?

A. 45\%
B. 37\%
C. 28\%
D. 14\%

Sagot :

GinnyAnswer
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].
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