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Will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. He found that 35 of the 99 students who own a skateboard have snowboarded. Also, there were 13 students who have snowboarded but do not own a skateboard, and 147 students who have never gone snowboarding and do not own a skateboard.

Which two-way table correctly displays this data?

\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}



Answer :

GinnyAnswer
To solve this problem, we need to carefully arrange the given information into a two-way table. Let's go through the data:

1. Given Data:
- 35 students own a skateboard and have snowboarded.
- 13 students have snowboarded but do not own a skateboard.
- 147 students do not own a skateboard and have never snowboarded.
- 99 students own a skateboard in total.

2. Calculations:
- To find the number of students who never snowboarded but own a skateboard, we subtract those who own a skateboard and have snowboarded from the total skateboard owners: [tex]\(99 - 35 = 64\)[/tex].
- The total number of students who have snowboarded is the sum of those who have snowboarded with and without skateboards: [tex]\(35 + 13 = 48\)[/tex].
- The total number of students who have never snowboarded includes those who have never snowboarded but own a skateboard and those who have never snowboarded and do not own a skateboard: [tex]\(64 + 147 = 211\)[/tex].
- To find the grand total of all surveyed students, sum the total who have snowboarded and the total who have never snowboarded: [tex]\(48 + 211 = 259\)[/tex].

3. Building the Two-Way Table:
Integrate all the calculated numbers:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Have \\ Snowboarded \end{tabular} & \begin{tabular}{c} Never \\ Snowboarded \end{tabular} & Total \\ \hline Skateboard & 35 & 64 & 99 \\ \hline No Skateboard & 13 & 147 & 160 \\ \hline Total & 48 & 211 & 259 \\ \hline \end{tabular} \][/tex]

Therefore, the correct two-way table corresponding to the given data is as follows:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Have \\ Snowboarded \end{tabular} & \begin{tabular}{c} Never \\ Snowboarded \end{tabular} & Total \\ \hline Skateboard & 35 & 64 & 99 \\ \hline No Skateboard & 13 & 147 & 160 \\ \hline Total & 48 & 211 & 259 \\ \hline \end{tabular} \][/tex]

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