Janie asked all of her classmates about the number of pets they have in their household. Her findings are shown in the table.
Number of Pets in Students' Households
| | 0 pets | 1 pet | 2 pets | More than 2 pets | Total |
| :----- | :----- | :---- | :---- | :---------------- | :---- |
| Boys | 8 | 4 | 3 | 0 | 15 |
| Girls | 7 | 6 | 5 | 2 | 20 |
| Total | 15 | 10 | 8 | 2 | 35 |
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 (1)
Determine if the survey represents quantitative data.
Calculate the percentage of girls and boys who do not own a pet and compare the percentages.
Calculate the total number of girls who own 2 or more pets and compare the result to 2.
Compare the number of girls who do not own a pet to the number of girls who own at least one pet.
The survey represents quantitative data. The survey represents quantitative data.
Explanation
Analyze each statement Let's analyze the given statements one by one using the data from the table.
The survey represents quantitative data.
Quantitative data is numerical and represents a measurable quantity. In this case, the data represents the number of pets, which is numerical. Therefore, this statement is potentially true.
There is a greater percentage of girls who do not own a pet than boys who do not own a pet.
We need to calculate the percentage of girls and boys who do not own a pet.
Number of boys who do not own a pet = 8
Total number of boys = 15
Percentage of boys who do not own a pet = 15 8 × 100 = 53.33%
Number of girls who do not own a pet = 7
Total number of girls = 20
Percentage of girls who do not own a pet = 20 7 × 100 = 35%
Since 53.33% > 35%, there is a greater percentage of boys who do not own a pet than girls who do not own a pet. Therefore, this statement is false.
The total number of girls who own 2 or more pets is 2.
Number of girls who own 2 pets = 5
Number of girls who own more than 2 pets = 2
Total number of girls who own 2 or more pets = 5 + 2 = 7
Since 7 = 2, this statement is false.
More girls do not own a pet than do own a pet.
Number of girls who do not own a pet = 7
Number of girls who own at least one pet = 20 - 7 = 13
Since 7 < 13, more girls own a pet than do not own a pet. Therefore, this statement is false.
Confirm the first statement Based on the analysis above, only the first statement is potentially true. Let's confirm if the data is quantitative or qualitative. Quantitative data is numerical and represents a measurable quantity. The number of pets is a measurable quantity, so the data is quantitative.
Final Answer Therefore, the correct statement is: The survey represents quantitative data.
Examples
Understanding data types is crucial in many real-world scenarios. For instance, when analyzing customer feedback, you might deal with both quantitative data (like ratings on a scale of 1 to 5) and qualitative data (like open-ended comments). Knowing how to differentiate and handle these data types allows businesses to gain meaningful insights and make informed decisions. In this case, recognizing that the number of pets is quantitative data helps us correctly interpret the survey results.
