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.

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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 1

The completed two-way frequency table is as follows: \[ \begin{array}{|c|c|c|c|}<br\ />\hline\ <br\ />\text{Own\ Phone}\ &\ \text{Yes}\ &\ \text{No}\ &\ \text{Total}\ \\<br\ />\hline\ <br\ />\text{Own\ TV}\ &\ 40\ &\ 60\ &\ 100\ \\<br\ />\hline\ <br\ />\text{No\ TV}\ &\ 20\ &\ 30\ &\ 50\ \\<br\ />\hline\ <br\ />\text{Total}\ &\ 60\ &\ 90\ &\ 150\ \\<br\ />\hline<br\ />\end{array} \]

Answer 2

## Step 1 The 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 2 First, 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 3 Next, 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 4 We 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 5 Next, 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 6 Finally, 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 7 Now, 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.

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