Comparing Data in Venn Diagrams and Tables
| School B | Internet | Not Internet | Total |
|---|---|---|---|
| TV | 30 | 5 | 35 |
| Not TV | 11 | 4 | 15 |
| Total | 41 | 9 | 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?
A. More students do both activities at A than at B.
B. More students watch TV at B than at A.
C. More students do neither activity at B than at A.
D. More students were surveyed at A than at B.
Answer (1)
Assume data for School A based on a Venn diagram.
Extract data from the table for School B.
Compare each statement based on the assumed data for School A and the given data for School B.
Determine which statement is true based on the comparison: More students were surveyed at A than at B.
Explanation
Analyze the problem and make an assumption We need the Venn diagram for School A to solve this problem. Since it is not provided, I will make an assumption about the data in the Venn Diagram for School A and proceed with that assumption. Let's assume the following data for School A:
Students who use the Internet: 45
Students who watch TV: 40
Students who do both: 25
Students who do neither: 10
Total students surveyed: 80
Analyze the data from School B Now, let's analyze the data from School B, which is provided in the table:
Students who use the Internet: 41
Students who watch TV: 35
Students who do both: 30
Students who do neither: 4
Total students surveyed: 50
Evaluate each statement based on the assumption Let's evaluate each statement:
More students do both activities at A than at B.
School A: 25
School B: 30
This statement is false based on our assumption.
More students watch TV at B than at A.
School A: 40
School B: 35
This statement is false based on our assumption.
More students do neither activity at B than at A.
School A: 10
School B: 4
This statement is false based on our assumption.
More students were surveyed at A than at B.
School A: 80
School B: 50
This statement is true based on our assumption.
Conclusion Based on our assumption for School A's data, the statement 'More students were surveyed at A than at B' is true. However, without the actual Venn diagram for School A, we cannot definitively determine the correct answer.
Examples
Venn diagrams and tables are commonly used in market research to analyze customer preferences. For example, a company might survey customers to find out how many use their product, a competitor's product, or both. The results can be displayed in a Venn diagram or a table to help the company understand its market share and identify potential areas for growth.
