To solve this problem, we need to complete the process step by step to ensure we construct the correct two-way table based on the given data.
### Given Data:
1. 35 students who own a skateboard have snowboarded.
2. 13 students do not own a skateboard but have snowboarded.
3. 99 students own a skateboard.
4. 147 students have never gone snowboarding and do not own a skateboard.
### Step-by-Step Solution:
Step 1: Calculate the number of students who have a skateboard and have never snowboarded.
- Total students who own a skateboard: 99
- Students who own a skateboard and have snowboarded: 35
- Therefore, students who own a skateboard but never snowboarded = 99 - 35 = 64
Step 2: Calculate the total number of students who do not own a skateboard.
- Students who have never snowboarded and do not own a skateboard: 147
- Students who have snowboarded but do not own a skateboard: 13
- Therefore, total students who do not own a skateboard = 147 + 13 = 160
Step 3: Calculate the overall totals for students.
- Total number of students who have snowboarded: Students who own a skateboard and have snowboarded (35) + Students who do not own a skateboard and have snowboarded (13) = 35 + 13 = 48
- Total number of students who have never snowboarded: Students who own a skateboard and have never snowboarded (64) + Students who do not own a skateboard and have never snowboarded (147) = 64 + 147 = 211
- Therefore, total number of students surveyed = Total number who have snowboarded (48) + Total number who have never snowboarded (211) = 48 + 211 = 259
### Constructing the Two-Way Table:
The two-way table should display the results as follows:
| | Have Snowboarded | Never Snowboarded | Total |
|--------------|------------------|-------------------|-------|
| Skateboard | 35 | 64 | 99 |
| No Skateboard| 13 | 147 | 160 |
| Total | 48 | 211 | 259 |
Comparing this with the given options, the table that correctly displays this data is the third one:
\begin{tabular}{|c|c|c|c|}
\hline & \begin{tabular}{c}
Have \\
Snowboarded
\end{tabular} & \begin{tabular}{c}
Never \\
Snowboarded
\end{tabular} & Total \\
\hline Skateboard & 35 & 64 & 99 \\
\hline No Skateboard& 13 & 147 & 160 \\
\hline Total & 48 & 211 & 259 \\
\hline
\end{tabular}
So, the correct answer is the third table.
