Let's break down the information given in the problem and verify the statements asked about the two-way frequency table.
Given Table:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
& \text{Wear Glasses} & \text{Do Not Wear Glasses} & \text{Total} \\
\hline
\text{Students} & 32 & 97 & 129 \\
\hline
\text{Teachers} & 4 & 2 & 6 \\
\hline
\text{Total} & 36 & 99 & 135 \\
\hline
\end{array}
\][/tex]
Let's analyze the given data and verify the statements:
1. A total of 6 teachers were polled.
- From the table, it is clear that the total number of teachers (from both categories: wear glasses and do not wear glasses) is 6.
- This statement is correct.
2. The row categories are "Wears Glasses" and "Do Not Wear Glasses."
- The row categories in the table are actually "Students" and "Teachers."
- This statement is incorrect because the row categories are not "Wears Glasses" and "Do Not Wear Glasses."
3. Two teachers do not wear glasses.
- From the table, it is evident that the number of teachers who do not wear glasses is 2.
- This statement is correct.
Thus, from the analysis, the correct statements about the two-way frequency table are:
- A total of 6 teachers were polled.
- Two teachers do not wear glasses.
