Two-Way Frequency Tables Notes and Worksheets - Lindsay Bowden - Free Printable

Let me work through each question step by step using the two-way frequency table.

The Table:
| | Passed | Failed | Total |
|---|---|---|---|
| Studied | 12 | 3 | 15 |
| Didn't Study | 1 | 14 | 15 |
| Total | 13 | 17 | 30 |

Question 1: How many students studied?
Looking at the "Studied" row, the total is 15.
Answer: 15

Question 2: How many students failed?
Looking at the "Failed" column, the total is 17.
Answer: 17

Question 3: How many students did not study and failed the test?
Looking at the intersection of "Didn't Study" row and "Failed" column: 14
Answer: 14

Question 4: What percentage of students did not study?
Students who didn't study = 15
Total students = 30
Percentage = (15/30) × 100 = 0.5 × 100 = 50%
Answer: 50%

Question 5: What percentage of students passed the test?
Students who passed = 13
Total students = 30
Percentage = (13/30) × 100 = 0.4333... × 100 ≈ 43.33%
Answer: 43.33% (or about 43%)

Question 6: Out of the students that passed the test, what percentage studied?
Students who passed = 13
Of those who passed, students who studied = 12
Percentage = (12/13) × 100 = 0.9231... × 100 ≈ 92.31%
Answer: 92.31% (or about 92%)

Question 7: What is the relative frequency of students who studied and passed the test?
Students who studied AND passed = 12
Total students = 30
Relative frequency = 12/30 = 0.4 (or 40%)
Answer: 0.4 or 40%

Question 8: What is the relative frequency of students who failed the test?
Students who failed = 17
Total students = 30
Relative frequency = 17/30 ≈ 0.5667 (or 56.67%)
Answer: 17/30 or approximately 0.57 or 57%

Question 9: Is there an association between studying for the test and passing the test?
Let's compare:
- Of students who studied: 12 out of 15 passed = 80%
- Of students who didn't study: 1 out of 15 passed = 6.67%

There's a huge difference! Students who studied had an 80% pass rate, while those who didn't study only had about 7% pass rate. This shows a strong association.
Answer: Yes, there is a strong association.

Question 10: Is this statement always true: If a student studies, they will pass the test.
Looking at the table: 12 students who studied passed, but 3 students who studied FAILED.
So the statement is NOT always true because some students who studied still failed.
Answer: No, it's not always true.

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Final Answer:
1. 15 students
2. 17 students
3. 14 students
4. 50%
5. 43.33% (or about 43%)
6. 92.31% (or about 92%)
7. 0.4 or 40%
8. 17/30 or approximately 0.57 or 57%
9. Yes, there is a strong association between studying and passing
10. No, the statement is not always true (3 students who studied still failed)