Survey of 9th and 10th Graders with Siblings
| | Has a Sibling | Does Not Have a Sibling | Total |
| :-------------------- | :------------ | :---------------------- | :---- |
| 9th Graders | 64 | 17 | 81 |
| 10th Graders | 52 | 23 | 75 |
| Total | 116 | 40 | 156 |
Which statements are correct about the two-way frequency table? Check all that apply.
A. The survey represents quantitative data.
B. There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.
C. The total number of students in the poll who have a sibling is 116.
D. Fifty-two 10th graders were polled.
E. More 9th graders were polled than 10th graders.
Answer (2)
Survey data is qualitative, not quantitative.
Percentage of 10th graders without siblings is greater than 9th graders without siblings: \frac{17}{81} \times 100"> 75 23 × 100 > 81 17 × 100 .
Total students with siblings: 116 .
More 9th graders were polled than 10th graders: 75"> 81 > 75 .
Statements 2, 3, and 5 are correct.
Explanation
Analyze the problem and data We are given a two-way frequency table that presents data about 9th and 10th graders and whether they have siblings. We need to evaluate several statements based on the data in the table to determine which ones are correct.
Evaluate statement 1 The first statement is: The survey represents quantitative data. Quantitative data is numerical data that can be measured or counted. In this case, the data represents categories (9th graders, 10th graders, having siblings, not having siblings), which are qualitative, not quantitative. Thus, this statement is incorrect.
Evaluate statement 2 The second statement is: There is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling. To evaluate this, we need to calculate the percentage of 10th graders without siblings and the percentage of 9th graders without siblings.
The percentage of 10th graders without siblings is 75 23 × 100 ≈ 30.67% .
The percentage of 9th graders without siblings is 81 17 × 100 ≈ 20.99% .
Since 20.99\%"> 30.67% > 20.99% , the statement is correct.
Evaluate statement 3 The third statement is: The total number of students in the poll who have a sibling is 116. Looking at the table, the total number of students with siblings is indeed 116. Thus, this statement is correct.
Evaluate statement 4 The fourth statement is: Fifty-two 10th graders were polled. The table shows that 52 tenth graders have siblings. However, the total number of 10th graders polled is 75. Thus, this statement is incorrect.
Evaluate statement 5 The fifth statement is: More 9th graders were polled than 10th graders. The total number of 9th graders is 81, and the total number of 10th graders is 75. Since 75"> 81 > 75 , this statement is correct.
Final Answer Based on our analysis, 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.
Examples
Two-way frequency tables are commonly used in surveys and data analysis to understand relationships between different categorical variables. For example, a school might survey students about their participation in extracurricular activities and their academic performance. The data can then be organized in a two-way table to see if there's a correlation between participation in extracurriculars and academic success. This type of analysis helps schools make informed decisions about resource allocation and program development, ensuring they support students' overall development effectively. By analyzing the frequencies and percentages, educators can identify trends and patterns that might not be immediately obvious, leading to more targeted interventions and support for students.
The correct statements are that there is a greater percentage of 10th graders without siblings compared to 9th graders, the total number of students with siblings is 116, and more 9th graders were polled than 10th graders. Therefore, statements B, C, and E are correct.
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