A random sample of students at North High School were polled on whether they prefer a 15-minute break between classes in the morning or in the afternoon. The results are shown in the frequency table.
| | Morning | Afternoon | Total |
| :---- | :------ | :-------- | :---- |
| 10th | 21 | 17 | 38 |
| 11th | 16 | 25 | 41 |
| 12th | 19 | 20 | 39 |
| Total | 56 | 62 | 118 |
What is the joint relative frequency for 11th graders who want the break in the afternoon? Round to the nearest percent.
A. 21%
B. 25%
C. 40%
D. 61%
Answer (1)
Find the number of 11th graders who prefer the afternoon break: 25.
Divide this number by the total number of students: 118 25 .
Multiply by 100 to express as a percentage: 118 25 × 100 ≈ 21.186% .
Round to the nearest percent: 21% .
Explanation
Understand the problem We are asked to find the joint relative frequency for 11th graders who prefer the afternoon break. This means we need to find the fraction of all students who are 11th graders and prefer the afternoon break.
Identify the relevant numbers From the table, we see that there are 25 students who are in 11th grade and prefer the afternoon break. The total number of students is 118.
Calculate the joint relative frequency To find the joint relative frequency, we divide the number of 11th graders who prefer the afternoon break by the total number of students: 118 25 .
Convert to percentage To express this as a percentage, we multiply by 100: 118 25 × 100 ≈ 21.186% .
Round to the nearest percent Rounding to the nearest percent, we get 21%.
State the final answer Therefore, the joint relative frequency for 11th graders who want the break in the afternoon, rounded to the nearest percent, is 21%.
Examples
Joint relative frequency is useful in analyzing survey data to understand the preferences of specific subgroups within a larger population. For example, a marketing team might use joint relative frequency to determine the proportion of female customers aged 18-24 who prefer a particular product flavor. This helps them tailor their marketing efforts to specific demographics, improving the effectiveness of their campaigns. Similarly, in educational research, it can help understand the proportion of students from a particular socioeconomic background who excel in STEM subjects, informing targeted educational interventions.
