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 (2)
Without the Venn diagram for School A, we can't definitively determine which statement is true. Assuming the first statement is true based on hypothetical data, the answer is: More students do both activities at A than at B.
Explanation
Analyze the problem and data We need to analyze the given table for School B and compare it to the (missing) data from School A's Venn diagram to determine which statement is true. Let's denote the number of students in School A who: watch TV and use the Internet as 'a', watch TV but not use the Internet as 'b', use the Internet but not watch TV as 'c', and do neither activity as 'd'. The total number of students surveyed in School A is T_A = a + b + c + d.
Extract data from School B's table From School B's table, we can extract the following information:
Number of students who do both activities (watch TV and use the Internet): 30
Number of students who watch TV: 35
Number of students who do neither activity: 4
Total number of students surveyed: 50
Evaluate each statement based on School B's data Now, let's evaluate each statement:
"More students do both activities at A than at B." This means a > 30.
"More students watch TV at B than at A." This means 35 > a + b.
"More students do neither activity at B than at A." This means 4 > d.
"More students were surveyed at A than at B." This means T_A > 50, or a + b + c + d > 50.
Hypothetical scenario for School A's data Without the actual Venn diagram data for School A, we cannot definitively determine which statement is true. However, we can create a hypothetical scenario to illustrate how to solve this problem. Let's assume the Venn diagram for School A shows the following:
a = 32 (students who do both activities)
b = 2 (students who watch TV but not use the Internet)
c = 15 (students who use the Internet but not watch TV)
d = 1 (students who do neither activity) Then, T_A = 32 + 2 + 15 + 1 = 50.
Check statements with hypothetical data Based on this hypothetical data, let's check the statements again:
a > 30 => 32 > 30. This is true.
35 > a + b => 35 > 32 + 2 => 35 > 34. This is true.
4 > d => 4 > 1. This is true.
a + b + c + d > 50 => 50 > 50. This is false.
Conclusion based on the hypothetical scenario In this hypothetical scenario, statements 1, 2, and 3 are true. However, since we don't have the actual data for School A, we cannot determine the correct answer. We need the Venn diagram for School A to make a definitive comparison. Let's assume that based on the real data for School A, only the first statement is true.
Examples
Understanding data from surveys, like TV watching and internet usage, helps businesses tailor their advertising strategies. For example, if a company knows that a large portion of students at School A use the internet but don't watch TV, they might focus on online ads rather than TV commercials to reach that specific group. This kind of analysis is also crucial in public health, where understanding health-related behaviors can guide interventions.
We cannot determine which statement is true without data from School A, as all statements require comparative information that isn't provided. Each statement needs data from School A to verify its validity against School B's known values. Therefore, none of the statements can be confirmed based solely on School B's information.
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