100 students who are in 9th or 10th grade were asked if they participated in at least one extracurricular activity (sports, music, or drama). 40 of the students are in 10th grade, but only 18 of these participate in at least one extracurricular activity. 32 of the 9th grade students participate in at least one extracurricular activity. create a two-way table    identify the variable and the categories represented in this problem. set up and fill in a two-way table to represent the frequencies in this problem.

There are 2 variables in this problem. One variable is the class number and other variable is the participation in extracurricular activities. Each variable has further two categories. There are two classes: Class 9 and 10. And students either participate or do not participate in extracurricular activities, which makes 2 categories. 

The best approach to solve this question is to build a table and start entering the given information in it. When the given data has been entered fill the rest on basis of the data you have.

18 students from grade 10 participate in at least one Extracurricular activities. This means the rest students i.e. 22 students from grade 10 do not participate in Extracurricular activities. 

32 students from grade 9 participate in at least one Extracurricular activities. This means total students who participate in at least one Extracurricular activities are 18 + 32 = 50 students.

The rest 50 students do not participate in at least one Extracurricular activities. From these 22 are from class 10. So the rest i.e. 28 are from class 9.

Based on this data we can fill the table as shown in image below.