A survey was conducted at a high school to study which instruments students are interested in learning. The data gathered is in the two-way table below:
| | Violin | Trumpet | Flute | Clarinet | Total |
| :-------- | :----- | :------ | :---- | :------- | :---- |
| Freshman | 4 | 2 | 1 | 2 | 9 |
| Sophomore | 2 | 1 | 3 | 3 | 9 |
| Junior | 3 | 3 | 4 | 1 | 11 |
| Senior | 5 | 1 | 2 | 3 | 11 |
| Total | 14 | 7 | 10 | 9 | 40 |
Based on this table, what is the relative frequency that a student is a sophomore who wants to learn the flute?
[?]%
Answer (2)
Identify the number of sophomores interested in the flute: 3.
Divide this number by the total number of students surveyed: 40 3 .
Multiply by 100 to get the percentage: 40 3 × 100 = 7.5 .
The relative frequency is 7.5 .
Explanation
Identify the relevant data From the table, we can see that there are 3 sophomores who want to learn the flute. The total number of students surveyed is 40.
Calculate the fraction To find the relative frequency, we divide the number of sophomores who want to learn the flute by the total number of students surveyed: 40 3
Convert to percentage To express this as a percentage, we multiply by 100: 40 3 × 100 = 7.5
State the final answer Therefore, the relative frequency that a student is a sophomore who wants to learn the flute is 7.5%.
Examples
In market research, understanding the relative frequency of customer preferences helps companies tailor their products and marketing strategies. For example, if a survey shows that 7.5% of customers prefer a certain product feature, the company can prioritize developing that feature to increase customer satisfaction and sales.
The relative frequency that a student is a sophomore who wants to learn the flute is calculated to be 7.5%. This is done by dividing the number of sophomores interested in the flute by the total number of students surveyed and converting it to a percentage. In this case, there are 3 sophomores who want to learn the flute out of a total of 40 students.
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