Let's analyze the data provided by Janie's survey and evaluate the given statements one by one.
### Step 1: Understand the Data Given
The table shows the number of pets owned by boys and girls in Janie's class:
- Total students: 35 (15 boys + 20 girls)
- Boys without pets: 8
- Girls without pets: 7
- Girls with 2 pets: 5
- Girls with more than 2 pets: 2
### Step 2: Calculating Percentages
- Percentage of boys who do not own a pet:
[tex]\[
\text{Percentage boys no pets} = \left(\frac{8}{35}\right) \times 100 \approx 22.86\%
\][/tex]
- Percentage of girls who do not own a pet:
[tex]\[
\text{Percentage girls no pets} = \left(\frac{7}{35}\right) \times 100 \approx 20\%
\][/tex]
### Step 3: Evaluating Statements
1. Statement: "The survey represents quantitative data."
- This statement is false. The table represents categorical data (qualitative data) about whether students own 0, 1, 2, or more than 2 pets.
2. Statement: "There is a greater percentage of girls who do not own a pet than boys who do not own a pet."
- We have calculated the percentages:
- Percentage of boys without pets: [tex]\( 22.86\% \)[/tex]
- Percentage of girls without pets: [tex]\( 20.0\% \)[/tex]
- [tex]\( 20.0\% < 22.86\% \)[/tex]
- This statement is false.
3. Statement: "The total number of girls who own 2 or more pets is 2."
- Adding the number of girls with exactly 2 pets and those with more than 2 pets: [tex]\( 5 + 2 = 7 \)[/tex]
- This statement is false.
4. Statement: "More girls do not own a pet than do own a pet."
- Girls without pets: 7
- Total girls: 20
- Girls with pets: [tex]\( 20 - 7 = 13 \)[/tex]
- Comparison: 7 (without pets) vs. 13 (with pets)
- This statement is false.
### Conclusion
Given the analysis:
- Statement 1: False
- Statement 2: False
- Statement 3: False
- Statement 4: False
Therefore, none of the statements about the two-way frequency table are true based on the given data and the calculations above.
