Question

comparing data in venn diagrams and tables
school a
venn diagram with two overlapping circles: left (internet) has 9, overlap (both) has 26, right (tv) has 12, outside both has 3
school b
two - way table with rows: tv, not tv, total; columns: internet, not internet, total. values: tv - internet: 30, tv - not internet: 5, tv - total: 35; not tv - internet: 11, not tv - not internet: 4, not tv - total: 15; total - internet: 41, total - not internet: 9, total - total: 50
students from school a and school b were asked whether they watch tv or use the internet after finishing their homework. the venn diagram and the two - way table show the results from the two surveys. which statement is true?
○ more students do both activities at a than at b.
○ more students watch tv at b than at a.
○ more students do neither activity at b than at a.
○ more students were surveyed at a than at b.

Explanation:

1. Analyze "More students do both activities at A than at B":

• For School A, the number of students doing both activities (Internet and TV) is 26 (from the Venn diagram).
• For School B, the number of students doing both activities (Internet and TV) is the number of students in the "TV" row and "Internet" column of the two - way table, which is 30. Since \(26<30\), this statement is false.

1. Analyze "More students watch TV at B than at A":

• For School A, the number of students who watch TV is the number of students in the "TV" circle, which is the sum of the students who only watch TV and those who do both. So it is \(12 + 26=38\).
• For School B, the number of students who watch TV is the total number of students in the "TV" row of the two - way table, which is 35. Since \(38>35\), this statement is false.

1. Analyze "More students do neither activity at B than at A":

• For School A, the number of students who do neither activity is 3 (from the Venn diagram, the number outside both circles).
• For School B, the number of students who do neither activity is the number of students in the "Not TV" row and "Not Internet" column of the two - way table, which is 4. Since \(4 > 3\), this statement is true.

1. Analyze "More students were surveyed at A than at B":

• For School A, the total number of students surveyed is the sum of all the numbers in the Venn diagram: \(9+26 + 12+3=50\).
• For School B, the total number of students surveyed is the total in the two - way table, which is 50. So the number of students surveyed at A and B is the same, and this statement is false.

Answer:

More students do neither activity at B than at A.