Question

a survey asked 40 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. 20 students are not in band.

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

	band	not in band	total
dont play instrument	0	15	15
total	20	20	40

b.

	band and play instrument	not in band and play instrument	total
band and dont play instrument	5	15	20
total	25	15	40

c.

	band	dont play instrument	total
play instrument	0	15	15
total	20	20	40

d.

	band	not in band	total
dont play instrument	5	15	20
total	25	15	40

Explanation:

Step1: Analyze total students

Total students are 40. For band: 20, not in band: 20. For play instrument: 25, don't play: \(40 - 25 = 15\).

Step2: Check each table

• Option A:
• Play instrument: Band = 20, Not in band = 5 (20 + 5 = 25, correct).
• Don't play instrument: Band = 0, Not in band = 15 (0 + 15 = 15, correct).
• Total Band: 20 + 0 = 20, Total Not in band: 5 + 15 = 20, Total students: 25 + 15 = 40. All totals match.
• Option B: Columns and rows are mislabeled (e.g., "Band and play instrument" as a column is incorrect for two - way table structure), so eliminate.
• Option C: Rows and columns are mislabeled (e.g., "Don't play instrument" as a column and "Not in band" as a row mix up categories), eliminate.
• Option D: Play instrument total is 20 (should be 25), Don't play instrument total is 20 (should be 15), Band total is 25 (should be 20), so incorrect.

Answer:

A.

	Band	Not in band	Total
Don't play instrument	0	15	15
Total	20	20	40