Let's analyze each statement step by step based on the data provided and the numerical results given:
### Data Provided
- Boys: 15 total
- No pets: 8
- 1 pet: 4
- 2 pets: 3
- More than 2 pets: 0
- Girls: 20 total
- No pets: 7
- 1 pet: 6
- 2 pets: 5
- More than 2 pets: 2
### Analysis of the Statements
1. The survey represents quantitative data.
- Analysis: Quantitative data refers to data that can be measured and expressed numerically. The data in the table categorizes students based on the number of pets they have, so it is categorical data, not quantitative.
- Conclusion: This statement is False.
2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
- Analysis: We need to calculate the percentage of each group.
- Percentage of girls who do not own a pet:
[tex]\[
\frac{7}{20} \times 100 = 35\%
\][/tex]
- Percentage of boys who do not own a pet:
[tex]\[
\frac{8}{15} \times 100 \approx 53.33\%
\][/tex]
- Comparing these percentages: [tex]\(35\% < 53.33\%\)[/tex]
- Conclusion: This statement is False.
3. The total number of girls who own 2 or more pets is 2.
- Analysis: From the table, the total number of girls who own 2 or more pets is the sum of girls with 2 pets and girls with more than 2 pets.
- Number of girls with 2 pets: 5
- Number of girls with more than 2 pets: 2
- Sum = [tex]\(5 + 2 = 7\)[/tex]
- Conclusion: This statement is False (since 7 is not equal to 2).
4. More girls do not own a pet than do own a pet.
- Analysis:
- Girls who do not own pets: 7
- Girls who own pets: 20 - 7 = 13
- Comparing these numbers: [tex]\(7 < 13\)[/tex]
- Conclusion: This statement is False.
### Final Assessment
The true statement about the two-way frequency table is none of the given options as all of them are false based on the data analysis.
