The two-way table represents data from a survey asking teachers whether they teach English, math, or both.
Subjects Taught
| | English | Not English | Total |
| :--------- | :------ | :---------- | :---- |
| Math | 34 | 22 | 56 |
| Not Math | 40 | 8 | 48 |
| Total | 74 | 30 | 104 |
Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent.
Answer (2)
Identify the number of teachers who teach math and not English: 22.
Determine the total number of teachers surveyed: 104.
Calculate the joint relative frequency: 104 22 ≈ 0.2115 .
Convert to percentage and round: 0.2115 × 100 ≈ 21% .
Explanation
Understand the problem and provided data We are given a two-way table that summarizes the results of a survey asking teachers whether they teach English, Math, or both. The table provides the number of teachers in each category. Our goal is to find the joint relative frequency for teachers who teach math and not English. This means we need to find the number of teachers who teach math and not English, and then divide that number by the total number of teachers surveyed. Finally, we need to express this fraction as a percentage, rounded to the nearest whole number.
Identify the required numbers from the table From the table, we can see that there are 22 teachers who teach math and not English. The total number of teachers surveyed is 104.
Calculate the joint relative frequency To find the joint relative frequency, we divide the number of teachers who teach math and not English by the total number of teachers: 104 22 = 0.211538...
Convert to percentage To express this as a percentage, we multiply by 100: 0.211538... × 100 = 21.1538...
Round to the nearest percent Finally, we round the percentage to the nearest whole number: 21.1538... ≈ 21 So, the joint relative frequency for teachers who teach math and not English, rounded to the nearest percent, is 21%.
State the final answer The joint relative frequency for teachers who teach math and not English is approximately 21%.
Examples
In educational research, joint relative frequency helps analyze survey data to understand the distribution of teacher specializations. For example, a school district might use this to determine the percentage of teachers who teach both math and science to better allocate resources and training programs. Knowing these percentages can inform decisions about staffing, curriculum development, and professional development opportunities, ensuring that teachers are well-prepared to meet the diverse needs of students.
The joint relative frequency for teachers who teach math and not English is calculated as approximately 21%. This is found by taking the number of teachers who teach math and not English (22) over the total teachers surveyed (104) and converting to a percentage. Finally, rounding gives us 21%.
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