Answered

Each grade level survey conducted with high school students in a particular area is shown below:

\begin{tabular}{|c|c|c|c|c|c|}
\cline{2-5}
& 9 & 10 & 11 & 12 & Total \\
\hline
Sports & 63 & 52 & 35 & 41 & \\
\hline
\begin{tabular}{c}
No \\ Sports
\end{tabular} & 51 & 45 & 21 & 36 & \\
\hline
Total & & & & & 344 \\
\hline
\end{tabular}

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

A. 191 students play sports and 150 students do not.
B. 153 students do not participate in sports and seventy-five 12th graders were surveyed.
C. 153 students do not participate in sports and 190 do.
D. 191 students play sports and ninety-seven 10th graders were surveyed.



Answer :

GinnyAnswer
Sure, let's solve the problem step-by-step and verify each statement.

### Step 1: Calculate the Total Number of Students Playing Sports

Add the number of students playing sports from each grade:
- 9th grade: 63
- 10th grade: 52
- 11th grade: 35
- 12th grade: 41

[tex]\[ \text{Total Sports} = 63 + 52 + 35 + 41 = 191 \][/tex]

### Step 2: Calculate the Total Number of Students Not Playing Sports

Add the number of students not playing sports from each grade:
- 9th grade: 51
- 10th grade: 45
- 11th grade: 21
- 12th grade: 36

[tex]\[ \text{Total No Sports} = 51 + 45 + 21 + 36 = 153 \][/tex]

### Step 3: Calculate the Total Number of 12th Grade Students Surveyed

Add the number of students in the 12th grade who play sports and those who do not:
[tex]\[ \text{Total 12th Grade} = 41 + 36 = 77 \][/tex]

### Step 4: Calculate the Total Number of 10th Grade Students Surveyed

Add the number of students in the 10th grade who play sports and those who do not:
[tex]\[ \text{Total 10th Grade} = 52 + 45 = 97 \][/tex]

### Step 5: Verify the Statements

1. 191 students play sports and 150 students do not
- Total Sports: 191 (Correct)
- Total No Sports: 150 (Incorrect, it's 153)

2. 153 students do not participate in sports and seventy-five 12th graders were surveyed
- Total No Sports: 153 (Correct)
- Total 12th Grade: 75 (Incorrect, it's 77)

3. 153 students do not participate in sports and 190 do.
- Total No Sports: 153 (Correct)
- Total Sports: 190 (Incorrect, it's 191)

4. 191 students play sports and ninety-seven 10th graders were surveyed.
- Total Sports: 191 (Correct)
- Total 10th Grade: 97 (Correct)

After comparing with the given statements, the correct statement is:

191 students play sports and ninety-seven 10th graders were surveyed.

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