a survey asked 50 students if they play an instrument and if they are in band. 1. 25 students play an…

a survey asked 50 students if they play an instrument and if they are in band. 1. 25 students play an instrument. 2. 20 students are in band. 3. 30 students are not in band. which table shows these data correctly entered in a two - way frequency table?

Answer

Explanation:

Step1: Analyze given data

We know total students = 50, students who play an instrument = 25, students in band = 20, students not in band = 30.

Step2: Check row - totals and column - totals for each option

Option A:

Row - totals and column - totals do not match the given data. For example, the total number of students who play an instrument in the table is 20 (band and play) + 0 (not in band and play) = 20, but we know 25 students play an instrument.

Option B:

The total number of students in band in the table is 20 (play instrument and in band)+0 (don't play instrument and in band) = 20. The total number of students who play an instrument is 20 (in band) + 5 (not in band)=25. The total number of students not in band is 5 (play instrument) + 25 (don't play instrument)=30. And the grand - total is 25 (play instrument) + 25 (don't play instrument)=50. This option satisfies all the given data.

Option C:

Row - totals and column - totals do not match the given data. For example, the total number of students who play an instrument in the table is 0 (in band) + 25 (not in band) = 25, but the way the categories are set up and the other values do not align with the given information about students in band and not in band.

Option D:

Row - totals and column - totals do not match the given data. For example, the total number of students in band in the table is 20 (play instrument and in band)+5 (don't play instrument and in band) = 25, but we know 20 students are in band.