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Question:

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

| | Enjoys swimming | Enjoys cycling | Row totals |
|----------------|-----------------|----------------|------------|
| Likes running | 28 | 62 | 90 |
| Does not like running | 46 | 64 | 110 |
| Column totals | 74 | 126 | 200 |

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

A. 45%
B. 35%
C. 20%
D. 14%



Answer :

GinnyAnswer
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].

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