To determine the correct two-way frequency table, we'll analyze the data step-by-step:
1. Total Students: There are 200 students in total—100 females and 100 males.
2. Females Enrolled in Algebra I: Out of the 100 female students, 57 are enrolled in Algebra I.
3. Remaining Females: The remaining females must be enrolled in Geometry.
[tex]\[
\text{Females in Geometry} = 100 - 57 = 43
\][/tex]
4. Males Enrolled in Geometry: Out of the 100 male students, 36 are enrolled in Geometry.
5. Remaining Males: The remaining males must be enrolled in Algebra I.
[tex]\[
\text{Males in Algebra I} = 100 - 36 = 64
\][/tex]
6. Calculating Totals for Each Course:
- For Algebra I:
[tex]\[
\text{Total enrolled in Algebra I} = 57 \text{ (females)} + 64 \text{ (males)} = 121
\][/tex]
- For Geometry:
[tex]\[
\text{Total enrolled in Geometry} = 43 \text{ (females)} + 36 \text{ (males)} = 79
\][/tex]
7. Constructing the Two-Way Frequency Table:
[tex]\[
\begin{array}{|l|c|c|c|}
\hline & \text{Algebra I} & \text{Geometry} & \text{Total} \\
\hline \text{Female} & 57 & 43 & 100 \\
\hline \text{Male} & 64 & 36 & 100 \\
\hline \text{Total} & 121 & 79 & 200 \\
\hline
\end{array}
\][/tex]
So the correct answer is:
\begin{tabular}{|l|c|c|c|}
\hline & Algebra I & Geometry & Total \\
\hline Female & 57 & 43 & 100 \\
\hline Male & 64 & 36 & 100 \\
\hline Total & 121 & 79 & 200 \\
\hline
\end{tabular}
