Answer :
Let's evaluate each statement based on the given data and analysis.
1. The survey represents quantitative data.
- The data represents the number of pets each student has, which is quantitative data (data that can be counted or measured).
- This statement is true.
2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
- To find the percentage of boys who do not own a pet:
[tex]\[ \text{Percentage of boys with no pets} = \left(\frac{8}{15}\right) \times 100 \approx 53.33\% \][/tex]
- To find the percentage of girls who do not own a pet:
[tex]\[ \text{Percentage of girls with no pets} = \left(\frac{7}{20}\right) \times 100 = 35\% \][/tex]
- Comparing these percentages, [tex]\(53.33\% > 35\%\)[/tex].
- This statement is false.
3. The total number of girls who own 2 or more pets is 2.
- Looking at the table, we see 5 girls have 2 pets, and 2 girls have more than 2 pets.
- Therefore, the total number of girls who own 2 or more pets is [tex]\(5 + 2 = 7\)[/tex].
- This statement is false.
4. More girls do not own a pet than do own a pet.
- According to the table, 7 girls do not own a pet.
- The total number of girls is 20, thus the number of girls who own a pet is [tex]\(20 - 7 = 13\)[/tex].
- Since 13 girls own a pet and 7 girls do not, more girls own a pet than do not.
- This statement is false.
Given this analysis, the only true statement about the two-way frequency table is:
- The survey represents quantitative data.
1. The survey represents quantitative data.
- The data represents the number of pets each student has, which is quantitative data (data that can be counted or measured).
- This statement is true.
2. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
- To find the percentage of boys who do not own a pet:
[tex]\[ \text{Percentage of boys with no pets} = \left(\frac{8}{15}\right) \times 100 \approx 53.33\% \][/tex]
- To find the percentage of girls who do not own a pet:
[tex]\[ \text{Percentage of girls with no pets} = \left(\frac{7}{20}\right) \times 100 = 35\% \][/tex]
- Comparing these percentages, [tex]\(53.33\% > 35\%\)[/tex].
- This statement is false.
3. The total number of girls who own 2 or more pets is 2.
- Looking at the table, we see 5 girls have 2 pets, and 2 girls have more than 2 pets.
- Therefore, the total number of girls who own 2 or more pets is [tex]\(5 + 2 = 7\)[/tex].
- This statement is false.
4. More girls do not own a pet than do own a pet.
- According to the table, 7 girls do not own a pet.
- The total number of girls is 20, thus the number of girls who own a pet is [tex]\(20 - 7 = 13\)[/tex].
- Since 13 girls own a pet and 7 girls do not, more girls own a pet than do not.
- This statement is false.
Given this analysis, the only true statement about the two-way frequency table is:
- The survey represents quantitative data.
