Join the IDNLearn.com community and get your questions answered by knowledgeable individuals. Our experts are ready to provide prompt and detailed answers to any questions you may have.

A survey asked 50 students if they play an instrument and if they are in the band.

1. 25 students play an instrument.
2. 20 students are in the band.
3. 30 students are not in the band.

Which table shows these data correctly entered in a two-way frequency table?

A.
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in Band & Total \\
\hline Play instrument & 20 & 5 & 25 \\
\hline Don't play instrument & 0 & 25 & 25 \\
\hline Total & 20 & 30 & 50 \\
\hline
\end{tabular}

B.
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in Band & Total \\
\hline Play instrument & 20 & 0 & 20 \\
\hline Don't play instrument & 5 & 25 & 30 \\
\hline Total & 25 & 25 & 50 \\
\hline
\end{tabular}

C.
\begin{tabular}{|l|c|c|c|}
\hline & Band and play instrument & Not in Band and play instrument & Total \\
\hline Not in Band and don't play instrument & 20 & 0 & 20 \\
\hline Band and don't play instrument & 5 & 25 & 30 \\
\hline Total & 25 & 25 & 50 \\
\hline
\end{tabular}

D.
\begin{tabular}{|l|c|c|c|}
\hline & Band & Don't play instrument & Total \\
\hline Not in Band & 20 & 5 & 25 \\
\hline Play instrument & 0 & 25 & 25 \\
\hline Total & 20 & 30 & 50 \\
\hline
\end{tabular}


Sagot :

To determine which table correctly represents the data from the survey, we need to fill in a two-way frequency table with the information given and inferred:

1. Total number of students surveyed: 50
2. Number of students who play an instrument: 25
3. Number of students who are in band: 20
4. Number of students who are not in band: 30

From the information, we can infer the following:
1. Number of students who play an instrument and are in band: 20
2. Number of students who play an instrument and are not in band: [tex]\( 25 - 20 = 5 \)[/tex]
3. Number of students who do not play an instrument and are in band: [tex]\( 20 - 20 = 0 \)[/tex]
4. Number of students who do not play an instrument and are not in band: [tex]\( 50 - 25 - 0 = 25 \)[/tex]

Now we can construct the correct table based on these calculations.

| | Band | Not in band | Total |
|-------------------|------|-------------|-------|
| Play instrument | 20 | 5 | 25 |
| Don't play instrument | 0 | 25 | 25 |
| Total | 20 | 30 | 50 |

Now let's match this with the provided options:

Option A:
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in Band & Total \\
\hline Play instrument & 20 & 5 & 25 \\
\hline Don't play instrument & 0 & 25 & 25 \\
\hline Total & 20 & 30 & 50 \\
\hline
\end{tabular}

This table exactly matches the data and our calculated values.

Option B:
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in band & Total \\
\hline Play instrument & 20 & 0 & 20 \\
\hline Don't play instrument & 5 & 25 & 30 \\
\hline Total & 25 & 25 & 50 \\
\hline
\end{tabular}

This table does not match the provided data or calculations as it misplaces the values.

Option C:
\begin{tabular}{|l|c|c|c|}
\hline & \begin{tabular}{l}
Band and\\play\\instrument
\end{tabular} & \begin{tabular}{c}
Not in band\\and play\\instrument
\end{tabular} & Total \\
\hline \begin{tabular}{l}
Not in band and\\don't play\\instrument
\end{tabular} & 20 & 0 & 20 \\
\hline \begin{tabular}{l}
Band and don't\\play instrument
\end{tabular} & 5 & 25 & 30 \\
\hline Total & 25 & 25 & 50 \\
\hline
\end{tabular}

This table arrangement and values are incorrect compared to our calculated values.

Option D:
\begin{tabular}{|l|c|c|c|}
\hline & Band & \begin{tabular}{l}
Don't play\\instrument
\end{tabular} & Total \\
\hline Not in band & 20 & 5 & 25 \\
\hline Play instrument & 0 & 25 & 25 \\
\hline Total & 20 & 30 & 50 \\
\hline
\end{tabular}

The labels and values are mixed up in this table compared to our calculations.

Therefore, the correct table is:

Option A:
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in Band & Total \\
\hline Play instrument & 20 & 5 & 25 \\
\hline Don't play instrument & 0 & 25 & 25 \\
\hline Total & 20 & 30 & 50 \\
\hline
\end{tabular}
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.