Question
Use the two-way frequency table to answer the question. What are the missing values?(1 point)
TV-Watching Preference Children Adults Total
Like to Watch TV
75 130
Don’t Like to Watch TV 84
152
Total 139 143 282
TV-Watching Preference Children Adults Total
Like to Watch TV
75 130
Don’t Like to Watch TV 84
152
Total 139 143 282
Answers
GPT-4o mini
To find the missing values in the two-way frequency table, we can fill in the blanks step-by-step using the information provided.
Let's start with the table we have:
| TV-Watching Preference | Children | Adults | Total |
|-------------------------------|----------|--------|-------|
| Like to Watch TV | 75 | 130 | ? |
| Don’t Like to Watch TV | 84 | ? | 152 |
| Total | 139 | 143 | 282 |
### Step 1: Calculate the total for "Like to Watch TV"
The total number of people who like to watch TV can be found by adding the children and adults that like to watch TV:
\[
Total\ of\ Like\ to\ Watch\ TV = Total\ Children - Don’t Like\ to\ Watch\ TV - Like\ to\ Watch\ TV
\]
The total is also given:
\[
Total\ of\ Like\ to\ Watch\ TV = Total - Don’t Like\ to\ Watch\ TV\ (Total)
\]
Thus, we can see:
\[
Total\ of\ Like\ to\ Watch\ TV = 282 - 152 = 130
\]
### Step 2: Fill in the missing "Like to Watch TV" total
We already have 75 from the "Children" row, therefore:
\[
Total\ of\ Like\ to\ Watch\ TV = 75 + 130 = 205\ (children\ +\ adults)
\]
Now we subtract this from the total population to find the missing total:
The total for the "Like to Watch TV" row is 130 + 75 = 205
**So the total number of people who like to watch TV is 130**.
### Step 3: Calculate the missing Adults in "Don't Like to Watch TV"
We can find the missing value for Adults who don't like to watch TV by subtracting the total number of children from the overall total:
Since we have
\[
Total\ of\ Don’t Like\ to Watch TVs = Adults\ +\ Children
\]
And we know:
\[
Total\ of\ Don’t Like\ to Watch TVs = 152,
\]
So
\[
84 + ? = 152 \Rightarrow ? = 152 - 84 = 68
\]
So for the adults who don’t like to watch TV, it is 68.
### Step 4: Fill in the tables with totals
Finally, the complete table looks like this:
| TV-Watching Preference | Children | Adults | Total |
|-------------------------------|----------|--------|-------|
| Like to Watch TV | 75 | 130 | 205 |
| Don’t Like to Watch TV | 84 | 68 | 152 |
| Total | 159 | 198 | 282 |
### Summary of missing values:
- Total for Like to Watch TV: 205
- Adults who don't like to watch TV: 68
Let me know if you need further assistance!
Let's start with the table we have:
| TV-Watching Preference | Children | Adults | Total |
|-------------------------------|----------|--------|-------|
| Like to Watch TV | 75 | 130 | ? |
| Don’t Like to Watch TV | 84 | ? | 152 |
| Total | 139 | 143 | 282 |
### Step 1: Calculate the total for "Like to Watch TV"
The total number of people who like to watch TV can be found by adding the children and adults that like to watch TV:
\[
Total\ of\ Like\ to\ Watch\ TV = Total\ Children - Don’t Like\ to\ Watch\ TV - Like\ to\ Watch\ TV
\]
The total is also given:
\[
Total\ of\ Like\ to\ Watch\ TV = Total - Don’t Like\ to\ Watch\ TV\ (Total)
\]
Thus, we can see:
\[
Total\ of\ Like\ to\ Watch\ TV = 282 - 152 = 130
\]
### Step 2: Fill in the missing "Like to Watch TV" total
We already have 75 from the "Children" row, therefore:
\[
Total\ of\ Like\ to\ Watch\ TV = 75 + 130 = 205\ (children\ +\ adults)
\]
Now we subtract this from the total population to find the missing total:
The total for the "Like to Watch TV" row is 130 + 75 = 205
**So the total number of people who like to watch TV is 130**.
### Step 3: Calculate the missing Adults in "Don't Like to Watch TV"
We can find the missing value for Adults who don't like to watch TV by subtracting the total number of children from the overall total:
Since we have
\[
Total\ of\ Don’t Like\ to Watch TVs = Adults\ +\ Children
\]
And we know:
\[
Total\ of\ Don’t Like\ to Watch TVs = 152,
\]
So
\[
84 + ? = 152 \Rightarrow ? = 152 - 84 = 68
\]
So for the adults who don’t like to watch TV, it is 68.
### Step 4: Fill in the tables with totals
Finally, the complete table looks like this:
| TV-Watching Preference | Children | Adults | Total |
|-------------------------------|----------|--------|-------|
| Like to Watch TV | 75 | 130 | 205 |
| Don’t Like to Watch TV | 84 | 68 | 152 |
| Total | 159 | 198 | 282 |
### Summary of missing values:
- Total for Like to Watch TV: 205
- Adults who don't like to watch TV: 68
Let me know if you need further assistance!