Question

what are the missing values in the following two-way frequency table?
sports particiaption: yes, no total
juniors: ___, 164, 476
seniors: 277, ____, 524
total: 589, 411, 1000

Answer 1

To find the missing values in the two-way frequency table, we can use the information already provided.

Here’s the layout of the table based on the information you provided:

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

### Step 1: Fill in the "Juniors" row
We know the total for juniors is 476. The number of juniors who participated in sports (Yes) can be found by subtracting the number of juniors who did not participate (No) from the total for juniors:

\[
\text{Juniors Yes} = \text{Total Juniors} - \text{Juniors No} = 476 - 164 = 312
\]

### Step 2: Fill in the "Seniors" row
We need to find the missing value for seniors who did not participate (No). We know the total for seniors is 524, and we can calculate the number of seniors who played sports (Yes) by subtracting from the total:

\[
\text{Seniors No} = \text{Total Seniors} - \text{Seniors Yes} = 524 - 277 = 247
\]

### Step 3: Verify totals
Now let's verify that the calculated values maintain the total counts:

1. **For sports participation (Yes)**:
- Juniors: 312
- Seniors: 277
- Total: \( 312 + 277 = 589 \) (which matches the given total)

2. **For sports participation (No)**:
- Juniors: 164
- Seniors: 247
- Total: \( 164 + 247 = 411 \) (which matches the given total)

### Final Table
The completed two-way frequency table is as follows:

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

### Summary of Missing Values:
- **Juniors Yes**: 312
- **Seniors No**: 247