To create the two-way frequency table, we will follow these steps to organize the given data across 9th grade, 10th grade, and total students, distinguishing between right-handed and left-handed students.
We are given the following information:
- Total students: 236
- 9th grade students: 121
- Right-handed students: 214
- Right-handed 10th grade students: 103
Using these details, we first need to find:
1. The number of 10th grade students.
2. The number of left-handed students.
3. The number of right-handed students in the 9th grade.
4. The number of left-handed students in the 9th grade.
5. The number of left-handed students in the 10th grade.
Here is the step-by-step solution:
1. Total number of 10th grade students:
[tex]\[
\text{Total 10th grade students} = 236 - 121 = 115
\][/tex]
2. Total left-handed students:
[tex]\[
\text{Left-handed students} = 236 - 214 = 22
\][/tex]
3. 9th grade right-handed students:
[tex]\[
\text{9th grade right-handed students} = 214 - 103 = 111
\][/tex]
4. 9th grade left-handed students:
[tex]\[
\text{9th grade left-handed students} = 121 - 111 = 10
\][/tex]
5. 10th grade left-handed students:
[tex]\[
\text{10th grade left-handed students} = 115 - 103 = 12
\][/tex]
Now we can fill in the two-way frequency table as follows:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Right-handed} & \text{Left-handed} & \text{Total} \\
\hline \text{9th Grade} & 111 & 10 & 121 \\
\hline \text{10th Grade} & 103 & 12 & 115 \\
\hline \text{Total} & 214 & 22 & 236 \\
\hline
\end{tabular}
\][/tex]
This table comprehensively categorizes the students based on their grade and whether they are right-handed or left-handed.
