A survey asked 60 students if they play an instrument and if they are in band.
1. 35 students play an instrument.
2. 30 students are in band.
3. 30 students are not in 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 & 30 & 5 & 35 \\
\hline Don't play instrument & 0 & 25 & 25 \\
\hline Total & 30 & 30 & 60 \\
\hline
\end{tabular}
B.
\begin{tabular}{|l|l|l|l|}
\hline & Band and play instrument & Not in band and piay instrument & Total \\
\hline Not in band and don't play instrument & 30 & 0 & 30 \\
\hline Band and don't play instrument & 5 & 25 & 30 \\
\hline Total & 35 & 25 & 60 \\
\hline
\end{tabular}
C.
\begin{tabular}{|l|c|c|c|}
\hline & Band & \begin{tabular}{c} Don't play \\ instrument \end{tabular} & Total \\
\hline Not in band & 30 & 5 & 35 \\
\hline Play instrument & 0 & 25 & 25 \\
\hline Total & 30 & 30 & 60 \\
\hline
\end{tabular}
D.
\begin{tabular}{|l|c|c|c|}
\hline & Band & Not in band & Total \\
\hline Play instrument & 30 & 0 & 30 \\
\hline Don't play instrument & 5 & 25 & 30 \\
\hline Total & 35 & 25 & 60 \\
\hline
\end{tabular}
Answer (1)
The problem requires identifying the correct two-way frequency table that represents the given data about students playing instruments and being in band. By analyzing each table and comparing it to the given information, Table A is found to be the only one that accurately represents the data.
Analyze the given data: 60 total students, 35 play an instrument, 30 are in band, and 30 are not in band.
Verify that Table A correctly represents the data: Play instrument (35), In band (30), Not in band (30), Total students (60).
Eliminate other tables based on incorrect labeling or mismatched data.
Conclude that Table A is the correct table: A .
Explanation
Understand the problem We are given a survey of 60 students regarding whether they play an instrument and whether they are in band. We need to determine which two-way frequency table correctly represents the given data.
List the given information The given information is:
Total number of students = 60
Number of students who play an instrument = 35
Number of students in band = 30
Number of students not in band = 30
Calculate the number of students who don't play an instrument We can deduce that the number of students who do not play an instrument is 60 - 35 = 25.
Analyze Table A Now, let's analyze each table:
Table A:
Band
Not in band
Total
Play instrument
30
5
35
Don't play instrument
0
25
25
Total
30
30
60
In this table:
Students who play instrument = 30 + 5 = 35 (Correct)
Students in band = 30 + 0 = 30 (Correct)
Students not in band = 5 + 25 = 30 (Correct)
Students who don't play instrument = 0 + 25 = 25 (Correct)
Total students = 35 + 25 = 60 (Correct)
This table seems to match all the given information.
Analyze Table B Table B:
Band and play instrument
Not in band and play instrument
Total
Not in band and don't play instrument
30
0
30
Band and don't play instrument
5
25
30
Total
35
25
60
This table is incorrectly labeled. The rows and columns do not represent the correct categories.
Analyze Table C Table C:
Band
Don't play instrument
Total
Not in band
30
5
35
Play instrument
0
25
25
Total
30
30
60
This table is also incorrectly labeled. The rows and columns do not represent the correct categories. Also, the total number of students who play instrument is 25, which is incorrect.
Analyze Table D Table D:
Band
Not in band
Total
Play instrument
30
0
30
Don't play instrument
5
25
30
Total
35
25
60
In this table:
Students who play instrument = 30 + 0 = 30 (Incorrect, should be 35)
Students in band = 30 + 5 = 35 (Incorrect, should be 30)
Students not in band = 0 + 25 = 25 (Incorrect, should be 30)
Students who don't play instrument = 5 + 25 = 30 (Correct)
Total students = 35 + 25 = 60 (Correct)
This table does not match the given information.
Conclusion Therefore, Table A is the only table that correctly represents the given data.
Examples
Two-way frequency tables are useful in organizing and analyzing data from surveys or experiments. For example, a marketing team could use a two-way table to analyze customer preferences for different product features, helping them to tailor their marketing strategies. Similarly, a school administrator could use a two-way table to analyze student performance in different subjects based on their participation in extracurricular activities, which could inform decisions about resource allocation and program development. These tables provide a clear and concise way to visualize relationships between different variables.
