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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.

Sagot :

GinnyAnsweridn
Let's analyze each of the statements in detail to determine which ones are correct based on the data provided in the table:

1. The survey represents quantitative data.

- This statement is incorrect. The survey provides categorical data because it classifies students based on whether they have a sibling or not and what grade they are in. Quantitative data refers to numerical data that can be measured and expressed as a number, such as height, weight, or temperature.

2. There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.

- To verify this statement, we need to calculate the percentage of 9th graders and 10th graders who do not have a sibling.
- For 9th graders:
[tex]\[ \text{Percentage of 9th graders without a sibling} = \left(\frac{17}{81}\right) \times 100 \approx 20.99\% \][/tex]
- For 10th graders:
[tex]\[ \text{Percentage of 10th graders without a sibling} = \left(\frac{23}{75}\right) \times 100 \approx 30.67\% \][/tex]
- Since [tex]\( 30.67\% \)[/tex] (percentage of 10th graders without a sibling) is greater than [tex]\( 20.99\% \)[/tex] (percentage of 9th graders without a sibling), this statement is correct.

3. The total number of students in the poll who have a sibling is 116.

- This statement is directly confirmed by the table.
- The total number of students who have a sibling is indeed [tex]\( 64 + 52 = 116 \)[/tex].
- Therefore, this statement is correct.

4. Fifty-two 10th graders were polled.

- This statement is incorrect. According to the table, 52 10th graders have a sibling. However, the total number of 10th graders polled is 75.

5. More 9th graders were polled than 10th graders.

- According to the table:
- Total number of 9th graders polled is 81.
- Total number of 10th graders polled is 75.
- Since 81 (number of 9th graders) is greater than 75 (number of 10th graders), this statement is correct.

In summary, the correct statements are:

- 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.
- More 9th graders were polled than 10th graders.
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