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

Number of Pets in Students' Households

\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 given information step-by-step:

1. Understanding the data:
- For Boys:
- 8 boys have 0 pets.
- 4 boys have 1 pet.
- 3 boys have 2 pets.
- 0 boys have more than 2 pets.
- Total boys: 15.
- For Girls:
- 7 girls have 0 pets.
- 6 girls have 1 pet.
- 5 girls have 2 pets.
- 2 girls have more than 2 pets.
- Total girls: 20.
- Combined:
- 15 students have 0 pets.
- 10 students have 1 pet.
- 8 students have 2 pets.
- 2 students have more than 2 pets.
- Total students: 35.

2. Calculating percentages of boys and girls who do not own a pet:
- Boys who do not own a pet:
- Out of 15 boys, 8 boys do not own a pet.
- Percentage: [tex]\( \frac{8}{15} \times 100 \approx 53.33\% \)[/tex].

- Girls who do not own a pet:
- Out of 20 girls, 7 girls do not own a pet.
- Percentage: [tex]\( \frac{7}{20} \times 100 = 35\% \)[/tex].

3. Number of girls who own 2 or more pets:
- Girls who own 2 pets: 5.
- Girls who own more than 2 pets: 2.
- Total number of girls who own 2 or more pets: [tex]\( 5 + 2 = 7 \)[/tex].

4. Evaluating statements:
- Statement 1: The survey represents quantitative data.
- This is incorrect; the survey represents categorical/qualitative data as it classifies students based on a non-numerical category (number of pets).

- Statement 2: There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
- This is incorrect; the percentage of boys who do not own a pet (53.33%) is greater than the percentage of girls who do not own a pet (35%).

- Statement 3: The total number of girls who own 2 or more pets is 2.
- This statement is incorrect; the total number of girls who own 2 or more pets is 7.

- Statement 4: More girls do not own a pet than do own a pet.
- This is incorrect; among girls, 7 do not own a pet, while [tex]\(6 + 5 + 2 = 13\)[/tex] own at least one pet.

Given all analyzed data:
- The correct statement is none of the above. The provided statements do not match the actual data and calculations.

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