A group of 200 ninth-grade students responded to a survey that asked which math course they were enrolled in. According to the data collected:
- 100 female students and 100 male students responded.
- 57 females were enrolled in Algebra I.
- 36 males were enrolled in Geometry.

Which answer shows these data correctly entered in a two-way frequency table?

A.
\begin{tabular}{|l|c|c|c|}
\hline & Algebra I & Geometry & Total \\
\hline Female & 57 & 43 & 100 \\
\hline Male & 43 & 36 & 100 \\
\hline Total & 100 & 79 & 200 \\
\hline
\end{tabular}

B. [tex]$\square$[/tex] Algebra I Geometry [tex]$\square$[/tex] Total



Answer :

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}