To determine which statement is true about the joint frequencies in the given table, we will analyze the data step-by-step and verify each statement.
### Step-by-step Analysis:
1. 9th Graders:
- Total students: 63
- Students preferring Science: 40
- Students preferring Math (9th graders) = Total students - Students preferring Science
[tex]\[
\text{Math (9th graders)} = 63 - 40 = 23
\][/tex]
2. 10th Graders:
- Total students: 26
- Students preferring Math: 18
- Students preferring Science (10th graders) = Total students - Students preferring Math
[tex]\[
\text{Science (10th graders)} = 26 - 18 = 8
\][/tex]
3. 11th Graders:
- Total students: 29
- Students preferring Science: 15
- Students preferring Math (11th graders) = Total students - Students preferring Science
[tex]\[
\text{Math (11th graders)} = 29 - 15 = 14
\][/tex]
4. 12th Graders:
- Total students: 67
- Students preferring Science: 32
- Students preferring Math (12th graders) = Total students - Students preferring Science
[tex]\[
\text{Math (12th graders)} = 67 - 32 = 35
\][/tex]
### Verifying the Statements:
1. Statement 1: Twenty-three 9th graders and fifteen 11th graders prefer math.
- 9th graders preferring math: 23 (correct)
- 11th graders preferring math: 14 (incorrect)
2. Statement 2: Fourteen 11th graders prefer math and eight 10th graders prefer science.
- 11th graders preferring math: 14 (correct)
- 10th graders preferring science: 8 (correct)
3. Statement 3: Thirty-five 12th graders prefer math and nine 10th graders prefer science.
- 12th graders preferring math: 35 (correct)
- 10th graders preferring science: 8 (incorrect)
4. Statement 4: Twenty-three 9th graders and thirty-two 12th graders prefer math.
- 9th graders preferring math: 23 (correct)
- 12th graders preferring math: 35 (incorrect)
From this analysis, we can see that Statement 2 is the only statement that correctly reflects the data in the table.
Therefore, the correct statement is:
Fourteen 11th graders prefer math and eight 10th graders prefer science.
