Janie asked all of her classmates about the number of pets they have in their household. Her findings are shown in the table.

\begin{tabular}{|c|c|c|c|c|c|}
\hline & 0 pets & 1 pet & 2 pets & \begin{tabular}{c}
More than 2 \\
pets
\end{tabular} & Total \\
\hline Boys & 8 & 4 & 3 & 0 & 15 \\
\hline Girls & 7 & 6 & 5 & 2 & 20 \\
\hline Total & 15 & 10 & 8 & 2 & 35 \\
\hline
\end{tabular}

Which statement about the two-way frequency table is true?

A. The survey represents quantitative data.
B. There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
C. The total number of girls who own 2 or more pets is 2.
D. More girls do not own a pet than do own a pet.



Answer :

Let's analyze the findings step by step and verify the statements concerning the two-way frequency table.

1. Percentage of Boys and Girls Who Do Not Own a Pet:

For boys:
- Total number of boys: 15
- Number of boys with 0 pets: 8
- Percentage of boys with 0 pets: [tex]\(\frac{8}{15} \times 100 \approx 53.33\%\)[/tex]

For girls:
- Total number of girls: 20
- Number of girls with 0 pets: 7
- Percentage of girls with 0 pets: [tex]\(\frac{7}{20} \times 100 = 35\%\)[/tex]

This indicates that a larger percentage of boys do not own pets compared to girls.

2. Total Number of Girls Who Own 2 or More Pets:
- Number of girls with exactly 2 pets: 5
- Number of girls with more than 2 pets: 2
- Total number of girls with 2 or more pets: [tex]\(5 + 2 = 7\)[/tex]

3. Majority of Girls Not Owning a Pet:
- Number of girls not owning a pet: 7
- Total number of girls: 20
- Since 7 out of 20 is 35%, which is less than 50%, less than half of the girls do not own a pet.

Given the detailed calculations and verifications, we can now examine each statement:

1. The survey represents quantitative data:
- The survey in question involves counting the number of pets, which is a categorical variable. Thus, 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:
- The percentage of boys not owning pets is approximately 53.33%, while the percentage for girls is 35%. Therefore, this statement is false.

3. The total number of girls who own 2 or more pets is 2:
- We calculated that the total number of girls with 2 or more pets is 7, which makes this statement false.

4. More girls do not own a pet than do own a pet:
- With only 7 out of 20 girls not owning a pet, this number does not exceed the 13 girls who own at least one pet. Therefore, this statement is false.

To conclude, none of the given statements about the two-way frequency table are true.