Question

representing data using a two - way frequency table
survey of 9th and 10th graders with siblings
which statements are correct about the two - way frequency table? check all that apply.
has a sibling|does not have a sibling|total
9th graders|64|17|81
10th graders|52|23|75
total|116|40|156
the survey represents quantitative data.
there is a greater percentage of 10th graders who do not have a sibling than 9th graders who do not have a sibling.
the total number of students in the poll who have a sibling is 116.
fifty - two 10th graders were polled.
more 9th graders were polled than 10th graders.

Explanation:

Step1: Analyze data - type

The survey data is about counts of students with and without siblings in different grades, which is categorical (qualitative) not quantitative. So the first statement is incorrect.

Step2: Calculate percentages

Percentage of 10th - graders without siblings: $\frac{23}{75}\approx 0.307$. Percentage of 9th - graders without siblings: $\frac{17}{81}\approx 0.21$. So there is a greater percentage of 10th - graders who do not have a sibling than 9th - graders who do not have a sibling. This statement is correct.

Step3: Check total with siblings

The total number of students who have a sibling is $64 + 52=116$. This statement is correct.

Step4: Check number of 10th - graders

The total number of 10th - graders polled is $52 + 23 = 75$, not 52. This statement is incorrect.

Step5: Compare number of 9th and 10th - graders

Number of 9th - graders polled is 81, number of 10th - graders polled is 75. So more 9th - graders were polled than 10th - graders. This statement is correct.

Answer:

There is a greater percentage of 10th - graders who do not have a sibling than 9th - graders who do not have a sibling; The total number of students in the poll who have a sibling is 116; More 9th - graders were polled than 10th - graders.