Question

What are the missing values in the following two-way frequency table?(1 point)
Sports Participation Juniors Seniors Total
Yes
__ 277 589
164 __ No
164
411
Total 476 524 1,000

Answer 1

To find the missing values in the two-way frequency table, we can use the information provided in the table and solve for the missing values based on the totals.

Here's the table again with the known and unknown values:

```
Sports Participation Juniors Seniors Total
Yes ? 277 589
No 164 ? ?
Total 476 524 1000
```

1. **Total for 'Yes' and 'No'**:

From the 'Total' row, we know:
- Total Juniors (Yes + No) = 476
- Total Seniors (Yes + No) = 524

Let's begin with the Seniors column where we have:
- Seniors who said 'Yes' = 277
- Seniors who said 'No' = ?

Let the number of Seniors who said 'No' be \( x \).

From the 'Total' column, we know:
\[
277 + x = 524
\]
Solving for \( x \):
\[
x = 524 - 277
\]
\[
x = 247
\]

So, the number of Seniors who said 'No' is 247.

Now the table looks like this:

```
Sports Participation Juniors Seniors Total
Yes ? 277 589
No 164 247 ?
Total 476 524 1000
```

2. **Total for 'No'**:

For the total of 'No', we know:
\[
164 + 247 = ?
\]
Calculating that gives:
\[
? = 411
\]

So the total number of responses that said 'No' is 411.

Now we can create the table:

```
Sports Participation Juniors Seniors Total
Yes ? 277 589
No 164 247 411
Total 476 524 1000
```

3. **Total for 'Yes'**:

Now we can find the missing Junior value who said 'Yes'. We know:
\[
? + 164 = 476
\]
Let \( y \) be the number of Juniors who said 'Yes':
\[
y = 476 - 164
\]
\[
y = 312
\]

So now we have:

```
Sports Participation Juniors Seniors Total
Yes 312 277 589
No 164 247 411
Total 476 524 1000
```

So the missing values in the table are:
- Juniors who said 'Yes': 312
- Seniors who said 'No': 247
- Total number of responses that said 'No': 411

Final filled table:

```
Sports Participation Juniors Seniors Total
Yes 312 277 589
No 164 247 411
Total 476 524 1000
```