Question
What are the missing values in the following two-way frequency table?(1 point)
This table presents data on sports participation among juniors and seniors, with some missing values, showing a total of 1000 students categorized by whether they participate in sports.
Sports Participation Juniors Seniors Total
Yes 277 589
No 164 411
Total 476 524 1,000
This table presents data on sports participation among juniors and seniors, with some missing values, showing a total of 1000 students categorized by whether they participate in sports.
Sports Participation Juniors Seniors Total
Yes 277 589
No 164 411
Total 476 524 1,000
Answers
GPT-4o mini
To find the missing values in the two-way frequency table, we can use the information provided to solve for the missing values logically.
Here's the current breakdown of the table:
```
Sports Participation Juniors Seniors Total
Yes 277 589
No 164 ?
Total 476 524 1000
```
1. **Calculating the missing value for seniors who do not participate in sports:**
Given that the total number of seniors is 524, we can find the missing value in the "No" row for seniors:
\[
\text{Total Seniors} = \text{Seniors who participate} + \text{Seniors who do not participate}
\]
We know the number of seniors who participate (Yes) is 589. Therefore, we can calculate:
\[
524 = 589 + \text{Seniors who do not participate}
\]
Solving for the missing value:
\[
\text{Seniors who do not participate} = 524 - 589 = -65
\]
Since the negative result does not make sense, we realize we need to look for this value correctly. We subtract the juniors' "No" participation from the total.
Total number of students who do not participate = 411, which also includes seniors.
2. **Finding the Total for No Participation:**
The total number of students who do not participate in sports is given as 411:
\[
\text{Total No} = \text{Juniors No} + \text{Seniors No} = 164 + \text{Seniors No}
\]
Therefore,
\[
411 = 164 + \text{Seniors No}
\]
To find "Seniors No":
\[
\text{Seniors No} = 411 - 164 = 247
\]
So, the missing value for seniors who do not participate in sports is **247**.
3. **Finally, completing the table:**
As a final review of the table, let’s complete it:
```
Sports Participation Juniors Seniors Total
Yes 277 589 866
No 164 247 411
Total 476 524 1000
```
Thus, the missing value in the table is as follows:
- Seniors who do not participate in sports: **247**.
Here's the current breakdown of the table:
```
Sports Participation Juniors Seniors Total
Yes 277 589
No 164 ?
Total 476 524 1000
```
1. **Calculating the missing value for seniors who do not participate in sports:**
Given that the total number of seniors is 524, we can find the missing value in the "No" row for seniors:
\[
\text{Total Seniors} = \text{Seniors who participate} + \text{Seniors who do not participate}
\]
We know the number of seniors who participate (Yes) is 589. Therefore, we can calculate:
\[
524 = 589 + \text{Seniors who do not participate}
\]
Solving for the missing value:
\[
\text{Seniors who do not participate} = 524 - 589 = -65
\]
Since the negative result does not make sense, we realize we need to look for this value correctly. We subtract the juniors' "No" participation from the total.
Total number of students who do not participate = 411, which also includes seniors.
2. **Finding the Total for No Participation:**
The total number of students who do not participate in sports is given as 411:
\[
\text{Total No} = \text{Juniors No} + \text{Seniors No} = 164 + \text{Seniors No}
\]
Therefore,
\[
411 = 164 + \text{Seniors No}
\]
To find "Seniors No":
\[
\text{Seniors No} = 411 - 164 = 247
\]
So, the missing value for seniors who do not participate in sports is **247**.
3. **Finally, completing the table:**
As a final review of the table, let’s complete it:
```
Sports Participation Juniors Seniors Total
Yes 277 589 866
No 164 247 411
Total 476 524 1000
```
Thus, the missing value in the table is as follows:
- Seniors who do not participate in sports: **247**.