A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.

Explanation:

The answer choices are:

You should build a two-way frequency table with:

It is not important if playing/not playing in the band are in columns or in rows; the important thing is they both must below either to different columns or to different rows. The same is valid for playing a sport.

Then, these two forms are good for the two-way frequency table:

Option 1:

                                 Play in the band   Do not play in the band  Total

Play sport

Do not play sport

Total

Option 2:

                                             Play sport    Do not play sport    Total

Play in the band

Do not play in the band

Total

As for the options:

        This is placing In a band and Play a sport in different columns, when they should be in different rows,

       This is placing not in a band and Play a Sport in different columns when they should be in different rows.

         This is placing In a band and Do not play a Sport in different columns when they should be in different rows.

        This correctly describes the survey: it corresponds to the option #1 above.

reasoning from several particular examples to establish a general principle