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Algebra I - MA3109 B.CR
Assignment
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Representing Data Using a Two-Way Frequency Table

Survey of 9th and 10th Graders with Siblings

Which statements are correct about the two-way frequency table? Check all that apply.
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & \begin{tabular}{c}
Has a \\
Sibling
\end{tabular} & \begin{tabular}{c}
Does Not \\
Have a \\
Sibling
\end{tabular} & Total \\
\hline
\begin{tabular}{c}
9th \\
Graders
\end{tabular} & 64 & 17 & 81 \\
\hline
\begin{tabular}{c}
10th \\
Graders
\end{tabular} & 52 & 23 & 75 \\
\hline
Total & 116 & 40 & 156 \\
\hline
\end{tabular}

- The survey represents quantitative data.
- There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.
- The total number of students in the poll who have a sibling is 116.
- Fifty-two 10th graders were polled.
- More 9th graders were polled than 10th graders.

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GinnyAnsweridn
Let's analyze the given two-way frequency table step-by-step to determine the correctness of the given statements:

### Two-Way Frequency Table Interpretation:

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 } \multicolumn{1}{c|}{} & \begin{tabular}{c}
Has a \\
Sibling
\end{tabular} & \begin{tabular}{c}
Does Not \\
Have a \\
Sibling
\end{tabular} & Total \\
\hline \begin{tabular}{c}
9th \\
Graders
\end{tabular} & 64 & 17 & 81 \\
\hline \begin{tabular}{c}
10th \\
Graders
\end{tabular} & 52 & 23 & 75 \\
\hline Total & 116 & 40 & 156 \\
\hline
\end{tabular}

Based on this table, let's evaluate each statement:

#### Statement 1: The total number of students in the poll who have a sibling is 116.
- Correct: The table shows that 64 ninth graders and 52 tenth graders have a sibling. Adding these, we get [tex]\(64 + 52 = 116\)[/tex].

#### Statement 2: Fifty-two 10th graders were polled.
- Incorrect: Actually, this statement is misleading. It should refer to the specific detail that 52 10th graders have a sibling. If we consider both with and without siblings, we find that [tex]\(52 + 23 = 75\)[/tex] 10th graders were polled.

#### Statement 3: More 9th graders were polled than 10th graders.
- Correct: The table indicates that 81 ninth graders and 75 tenth graders were polled. Since 81 is greater than 75, this statement is true.

#### Statement 4: There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.
- Correct:
- Percentage of 9th graders without a sibling: [tex]\(\frac{17}{81} \times 100 \approx 20.99\%\)[/tex]
- Percentage of 10th graders without a sibling: [tex]\(\frac{23}{75} \times 100 \approx 30.67\%\)[/tex]

The percentage for 10th graders without a sibling is higher than that for the 9th graders.

### Summary:

- Correct Statements:
1. The total number of students in the poll who have a sibling is 116.
2. More 9th graders were polled than 10th graders.
3. There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.

- Incorrect Statement:
- Fifty-two 10th graders were polled (not accurate in context, needs clarification as 75 tenth graders were polled in total).

Thus, the correct statements, after thorough interpretation of the table, are clearly delineated.
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