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Problem Analysis:

The task involves interpreting a line plot that shows the number of hours each student in a class spent playing video games per month. Each "X" represents one student, and the key indicates that "X = 3 students." Using this information, we will answer the given questions step by step.

Line Plot Breakdown:

- Hours Spent per Student: The x-axis represents the number of hours (1 to 7).
- Frequency: Each "X" represents 3 students.
- Total Students per Hour:
- 1 hour: 2 "X"s → \(2 \times 3 = 6\) students
- 2 hours: 2 "X"s → \(2 \times 3 = 6\) students
- 3 hours: 4 "X"s → \(4 \times 3 = 12\) students
- 4 hours: 5 "X"s → \(5 \times 3 = 15\) students
- 5 hours: 4 "X"s → \(4 \times 3 = 12\) students
- 6 hours: 3 "X"s → \(3 \times 3 = 9\) students
- 7 hours: 2 "X"s → \(2 \times 3 = 6\) students

Total Number of Students:

Summing up all the students:
\[
6 + 6 + 12 + 15 + 12 + 9 + 6 = 66 \text{ students}
\]

Solving Each Question:

#### 1. To the nearest tenth percent, how many students played for exactly 4 hours?
- Students who played for 4 hours: 15 students.
- Percentage of students:
\[
\frac{15}{66} \times 100 \approx 22.7\%
\]
Answer: \(22.7\%\)

#### 2. Did more students play for fewer than 4 hours or more than 4 hours?
- Fewer than 4 hours:
- 1 hour: 6 students
- 2 hours: 6 students
- 3 hours: 12 students
- Total: \(6 + 6 + 12 = 24\) students
- More than 4 hours:
- 5 hours: 12 students
- 6 hours: 9 students
- 7 hours: 6 students
- Total: \(12 + 9 + 6 = 27\) students
- Comparison: 24 students (fewer than 4 hours) vs. 27 students (more than 4 hours).
Answer: More students played for more than 4 hours.

#### 3. How many students spent exactly 2 hours or 4 hours gaming?
- 2 hours: 6 students
- 4 hours: 15 students
- Total: \(6 + 15 = 21\) students
Answer: 21 students

#### 4. How many students spent exactly 6 hours or 3 hours gaming?
- 3 hours: 12 students
- 6 hours: 9 students
- Total: \(12 + 9 = 21\) students
Answer: 21 students

#### 5. To the nearest tenth percent, how many students played 3 hours or less?
- 1 hour: 6 students
- 2 hours: 6 students
- 3 hours: 12 students
- Total: \(6 + 6 + 12 = 24\) students
- Percentage:
\[
\frac{24}{66} \times 100 \approx 36.4\%
\]
Answer: \(36.4\%\)

#### 6. In total, how many hours were spent gaming by all students?
- Calculate total hours for each group:
- 1 hour: \(6 \times 1 = 6\) hours
- 2 hours: \(6 \times 2 = 12\) hours
- 3 hours: \(12 \times 3 = 36\) hours
- 4 hours: \(15 \times 4 = 60\) hours
- 5 hours: \(12 \times 5 = 60\) hours
- 6 hours: \(9 \times 6 = 54\) hours
- 7 hours: \(6 \times 7 = 42\) hours
- Total hours:
\[
6 + 12 + 36 + 60 + 60 + 54 + 42 = 370 \text{ hours}
\]
Answer: 370 hours

#### 7. What was the most common number of hours spent on video games per student?
- From the line plot, the highest frequency is for 4 hours, with 15 students.
Answer: 4 hours

#### 8. How many students played for at least 3 hours?
- At least 3 hours:
- 3 hours: 12 students
- 4 hours: 15 students
- 5 hours: 12 students
- 6 hours: 9 students
- 7 hours: 6 students
- Total: \(12 + 15 + 12 + 9 + 6 = 54\) students
Answer: 54 students

#### 9. What was the least common number of hours spent gaming per student?
- The lowest frequency is for 1 hour and 7 hours, both with 6 students.
Answer: 1 hour and 7 hours

#### 10. Rounded to the nearest hundredth, what is the mean number of time spent gaming per student?
- Mean is calculated as:
\[
\text{Mean} = \frac{\text{Total Hours}}{\text{Total Students}} = \frac{370}{66} \approx 5.61
\]
Answer: 5.61

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 22.7\% \\
2. & \text{More students played for more than 4 hours.} \\
3. & 21 \\
4. & 21 \\
5. & 36.4\% \\
6. & 370 \\
7. & 4 \\
8. & 54 \\
9. & 1 \text{ and } 7 \\
10. & 5.61 \\
\end{array}
}
\]