A survey was conducted at a high school to study pet ownership in different grade levels. The data gathered is in the two-way table below:
| | Dog | Cat | No Pet | Total |
| :-------- | :-- | :-- | :----- | :---- |
| Freshman | 3 | 3 | 5 | 11 |
| Sophomore | 5 | 7 | 4 | 16 |
| Junior | 8 | 1 | 3 | 12 |
| Senior | 2 | 3 | 6 | 11 |
| Total | 18 | 14 | 18 | 50 |
Based on this table, what is the relative frequency that a student is a sophomore who has a cat?
Answer (2)
Find the number of sophomores who own a cat: 7.
Find the total number of students: 50.
Calculate the relative frequency: 50 7 × 100 .
The relative frequency is 14 % .
Explanation
Identify the relevant data First, let's identify the number of students who are sophomores and own a cat. Looking at the table, we see that there are 7 sophomores who own a cat.
Find the total number of students Next, we need to find the total number of students surveyed. The table shows that there are a total of 50 students.
Calculate the relative frequency Now, we will calculate the relative frequency by dividing the number of sophomores who own a cat by the total number of students, and then multiply by 100 to express the result as a percentage.
50 7 = 0.14
0.14 × 100 = 14
State the final answer Therefore, the relative frequency that a student is a sophomore who has a cat is 14%.
Examples
Understanding relative frequencies is useful in many real-world scenarios. For example, if a school wants to start a new club, they could survey students to see what activities are most popular. If 14% of students are interested in a coding club, the school knows that there is a good base of students to start the club. This helps the school make informed decisions about resource allocation and program development.
The relative frequency that a student is a sophomore who has a cat is 14%. This is calculated by dividing the 7 sophomores who have cats by the total of 50 surveyed students and converting it into a percentage. Thus, the final result is 14%.
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