Question
You survey students about whether they have their own phone or TV. According to the survey results: - 100 of the students have their own phone, and 60 of those students do not have their own TV - 50 of the students do not have their own phone, and 20 of those students have their own TV Organize the results in a two-way table. Include the marginal frequencies.
Answer
4.1
(264 Votes)
Jasper
Elite · Tutor for 8 years
Answer
The completed two-way frequency table is as follows:
Explanation
## Step 1The problem provides us with two sets of data:- 100 students own a phone, out of which 60 do not own a TV.- 50 students do not own a phone, out of which 20 own a TV.To organize this information, we need to create a two-way frequency table. This table will have two rows (representing the two categories of phone ownership: 'Yes' and 'No') and two columns (representing the two categories of TV ownership: 'Yes' and 'No').## Step 2First, we fill in the intersection of 'Phone: Yes' and 'TV: No' with the number of students who own a phone but do not own a TV, which is 60.## Step 3Next, we calculate the number of students who own a phone and also own a TV. This is done by subtracting the number of students who own a phone but do not own a TV (60) from the total number of students who own a phone (100). This gives us 40 students who own both a phone and a TV.## Step 4We then fill in the intersection of 'Phone: No' and 'TV: Yes' with the number of students who do not own a phone but do own a TV, which is 20.## Step 5Next, we calculate the number of students who do not own a phone and do not own a TV. This is done by subtracting the number of students who do not own a phone but own a TV (20) from the total number of students who do not own a phone (50). This gives us 30 students who do not own either a phone or a TV.## Step 6Finally, we fill in the intersection of 'Phone: No' and 'TV: No' with the number of students who do not own either a phone or a TV, which is 30.## Step 7Now, we can calculate the marginal frequencies. The marginal frequency is the total number of students in each row and column. For example, the total number of students who own a phone is the sum of the students who own a phone and a TV (40) and the students who own a phone but not a TV (60), which is 100. Similarly, we can calculate the total number of students who do not own a phone (50), the total number of students who own a TV (60), and the total number of students who do not own a TV (90). The total number of students surveyed is the sum of the students who own a phone (100) and the students who do not own a phone (50), which is 150.