To create a relative frequency table by row from the given frequency table, we need to calculate the percentage of each category with respect to the total for each row. Here is the step-by-step process:
### Given Frequency Table
| | Algebra | Geometry | Total |
|----------|---------|----------|-------|
| Biology | 67 | 25 | 92 |
| Chemistry| 46 | 20 | 66 |
| Total | 113 | 45 | 158 |
### Step-by-Step Calculation
1. Biology Row
- Algebra Percentage:
[tex]\[
\left( \frac{67}{92} \right) \times 100 \approx 72.826
\][/tex]
- Geometry Percentage:
[tex]\[
\left( \frac{25}{92} \right) \times 100 \approx 27.174
\][/tex]
- Total: 100% (By definition, each row sums up to 100%)
2. Chemistry Row
- Algebra Percentage:
[tex]\[
\left( \frac{46}{66} \right) \times 100 \approx 69.697
\][/tex]
- Geometry Percentage:
[tex]\[
\left( \frac{20}{66} \right) \times 100 \approx 30.303
\][/tex]
- Total: 100% (By definition, each row sums up to 100%)
With these calculations, the relative frequency table by row will look like this:
### Relative Frequency Table By Row
| | Algebra | Geometry | Total |
|----------|----------|----------|-------|
| Biology | 72.83% | 27.17% | 100% |
| Chemistry| 69.70% | 30.30% | 100% |
### Filling the Tiles
Now let's match the values to the tiles provided:
1. 100%: This is placed in the 'Total' column for both Biology and Chemistry.
2. 73% (approx 72.83%): This is placed in the Biology 'Algebra' cell.
3. 70% (approx 69.70%): This is placed in the Chemistry 'Algebra' cell.
4. 27% (approx 27.17%): This is placed in the Biology 'Geometry' cell.
5. 30% (approx 30.30%): This is placed in the Chemistry 'Geometry' cell.
So the final table with tiles filled in would be:
### Final Relative Frequency Table
| | Algebra | Geometry | Total |
|----------|---------|----------|-------|
| Biology | 73% | 27% | 100% |
| Chemistry| 70% | 30% | 100% |
This representation reflects the relative frequency distribution of students' preferences for algebra and geometry within biology and chemistry classes.
