A survey asked 50 students if they play an instrument and if they are in band.25 students play an instrument.20 students are in band.30 students are not in band.Which table shows these data correctly entered in a two-way frequency table?
Question
A survey asked 50 students if they play an instrument and if they are in band.25 students play an instrument.20 students are in band.30 students are not in band.Which table shows these data correctly entered in a two-way frequency table?
Solution
A two-way frequency table for this data would look like this:
| Play an Instrument | Don't Play an Instrument | Total | |
|---|---|---|---|
| In Band | ? | ? | 20 |
| Not in Band | ? | ? | 30 |
| Total | 25 | ? | 50 |
To fill in the table, we need to find the values for the question marks.
-
First, we know that 20 students are in band. Since we don't know how many of these students play an instrument, we can't fill in this information yet.
-
We know that 30 students are not in band. Again, we don't know how many of these students play an instrument, so we can't fill in this information yet.
-
We know that 25 students play an instrument. We don't know how many of these students are in band or not in band, so we can't fill in this information yet.
-
We know that there are 50 students in total. Since 25 of them play an instrument, that means 25 students don't play an instrument. We can fill in this information in the "Total" row under "Don't Play an Instrument".
| Play an Instrument | Don't Play an Instrument | Total | |
|---|---|---|---|
| In Band | ? | ? | 20 |
| Not in Band | ? | ? | 30 |
| Total | 25 | 25 | 50 |
- Now, we can figure out the rest of the values. Since 20 students are in band and we know that 25 students don't play an instrument, that means that the number of students who are in band and don't play an instrument is 20 - 25 = -5. However, this is not possible, so there must be a mistake in the question.
Therefore, it is not possible to create a correct two-way frequency table with the given data.
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