Poll of Students and Teachers Who Wear Glasses
| | Wear Glasses | Do Not Wear Glasses | Total |
| :------- | :----------- | :------------------ | :---- |
| Students | 32 | 97 | 129 |
| Teachers | 4 | 2 | 6 |
| Total | 36 | 99 | 135 |
Which statements are correct about the two-way frequency table? Check all that apply.
A. The table displays qualitative data.
B. The row categories are "Wears Glasses" and "Do Not Wear Glasses."
C. Two teachers do not wear glasses.
D. Thirty-six students wear glasses.
E. A total of 6 teachers were polled.
Answer (2)
The table displays qualitative data.
Two teachers do not wear glasses.
A total of 6 teachers were polled.
The other statements are incorrect based on the data in the table. The table displays qualitative data, Two teachers do not wear glasses, A total of 6 teachers were polled.
Explanation
Analyze the type of data displayed The table displays data categorized by whether individuals wear glasses or not, and whether they are students or teachers. This is qualitative data because it deals with categories rather than numerical measurements.
Verify row categories The rows are categorized by 'Students' and 'Teachers', not 'Wears Glasses' and 'Do Not Wear Glasses'. The columns are categorized by 'Wear Glasses' and 'Do Not Wear Glasses'.
Check the number of teachers who do not wear glasses According to the table, 2 teachers do not wear glasses.
Check the number of students who wear glasses The table indicates that 32 students wear glasses, not 36.
Verify the total number of teachers polled The table shows a total of 6 teachers were polled.
Examples
Two-way frequency tables are useful in surveys and data analysis to understand relationships between different categorical variables. For example, a school might use a two-way table to analyze the relationship between students' participation in extracurricular activities and their academic performance. This can help identify trends and inform decisions about resource allocation and program development. The data is organized to show how many students participate in each activity and their corresponding grade levels, providing insights into the impact of extracurricular involvement on academic success.
The correct statements from the table analysis are that it displays qualitative data, two teachers do not wear glasses, and a total of 6 teachers were polled. The statement about the row categories is incorrect as they are 'Students' and 'Teachers', while 32 students wear glasses, not 36. Therefore, statements A, C, and E are correct.
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