Question

1. 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

(a) Identify the variable and the categories represented in this problem.
(b) Set up and fill in a two-way table to represent the frequencies in this problem.

Answer 1

You are given such data:

In 10th grade of total 40 students only 18 students participate in at least one extracurricular activity and 40-18=22 students do not participate.

In 9th grade of total 100-40=60 students only 32 students participate in at least one extracurricular activity and 60-32=28 students do not participate.

Then two-way table is

`\begin{array}{cccc}&\text{Participate}&\text{Not Participate}&\text{Total}\\\text{10th Grade}&18&22&40\\\text{9th Grade}&32&28&60\\\text{Total}&50&50&100\end{array}`

There are two categorical variables - Grade and Participation.

Two-way frequency table is

`\begin{array}{cccc}&\text{Participate}&\text{Not Participate}&\text{Total}\\ \\\text{10th Grade}&(18)/(100)(=18\%)&(22)/(100)(=22\%)&(40)/(100)(=40\%)\\ \\\text{9th Grade}&(32)/(100)(=32\%)&(28)/(100)(=28\%)&(60)/(100)(=60\%)\\ \\\text{Total}&(50)/(100)(=50\%)&(50)/(100)(=50\%)&(100)/(100)(=100\%)\end{array}`