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.
