Answered

A survey was conducted with high school students in each grade to see how many prefer math or science. Some of the data are shown below.

\begin{tabular}{|c|c|c|c|c|c|}
\cline {2-5}
& 9 & 10 & 11 & 12 & Total \\
\hline Math & & 18 & & & 90 \\
\hline Science & 40 & & 15 & 32 & 95 \\
\hline Total & 63 & 26 & 29 & 67 & 185 \\
\hline
\end{tabular}

Which statement is true about the joint frequencies in this table?

A. Twenty-three 9th graders and fifteen 11th graders prefer math.
B. Fourteen 11th graders prefer math and eight 10th graders prefer science.
C. Thirty-five 12th graders prefer math and nine 10th graders prefer science.
D. Twenty-three 9th graders and thirty-two 12th graders prefer math.



Answer :

GinnyAnswer
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.

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