Ask easy yes or no questions to make a simple two-way table.
See solution.
Practice makes perfect
We were asked to create and conduct a survey. Since a lot of people have pets, we created a survey about that. We asked each student in the class if they have a dog or a cat. To create a two-way table, we will write the answer to each question as a header. Let's make it!
Has a Dog
Does Not Have a Dog
Has a Cat
Does Not Have a Cat
There were 50 students who took our survey. Here are the results.
10 students have a dog and a cat.
12 students have a dog, but do not have a cat.
7 students do not have a dog, but have a cat.
21 students do not have a dog or a cat.
Each of these numbers is a joint frequency. Let's add these values to the table in the appropriate cells.
Has a Dog
Does Not Have a Dog
Has a Cat
10
7
Does Not Have a Cat
12
21
Finally, to find the marginal frequencies, we will add the joint frequencies from each row and each column.
Has a Dog
Does Not Have a Dog
Total
Has a Cat
10
7
10+ 7 = 17
Does Not Have a Cat
12
21
12+ 21 = 33
Total
10+ 12 = 22
7+ 21 = 28
50
Any survey with categorical responses can have the results displayed in a two-way table with joint and marginal frequencies which are found in the same way. This is just one example.
