Question

the band leader is recording the number of students in the seventh and eighth grades who play flute and clarinet. which describes the variables in the two - way table?
band assignments

	flute	clarinet	total
8th grade	22	18	40
total

options:

• type of instrument and total number of seventh and eighth graders
• type of instrument and total number of seventh graders
• grade number and number of clarinet players
• grade number and type of instrument

Explanation:

To determine the variables in the two - way table, we analyze the rows and columns. The rows represent different grade levels (7th and 8th grade), so one variable is the grade number. The columns represent different types of instruments (Flute and Clarinet), so the other variable is the type of instrument.

• Option 1: "Total number of seventh and eighth graders" is a summary statistic, not a variable defining the table's structure. The table is about the number of students in each grade - instrument combination, not just the total of all students.
• Option 2: "Total number of seventh graders" is a summary for one grade, not a variable that defines the table's categories. The table has data for both 7th and 8th grades across different instruments.
• Option 3: "Number of clarinet players" is a specific count within the table, not a variable that defines the table's rows and columns. The rows are about grade levels, not just related to clarinet players.
• Option 4: The rows are grade numbers (7th, 8th) and the columns are types of instruments (Flute, Clarinet), so this option correctly identifies the two variables.

Answer:

D. grade number and type of instrument (assuming the last option is labeled D, if the original options were labeled A - D with the last one being "grade number and type of instrument")