Relative frequency table derived from a two-way frequency table, illustrating the proportion of students selecting each superpower by gender.

Problem Overview:

We are tasked with calculating the relative frequencies for each cell in a two-way frequency table. The relative frequency of a cell is determined by dividing the frequency of that cell by the total number of observations (in this case, 450). The goal is to complete the relative frequency table based on the provided two-way frequency table.

Given Data:

#### Two-Way Frequency Table:
| | To Fly | Freeze Time | Invisibility | Super Strength | Telepathy | Total |
|-----------|--------|-------------|--------------|----------------|------------|-------|
| Females | 49 | 60 | 48 | 1 | 70 | 228 |
| Males | 51 | 71 | 27 | 25 | 48 | 222 |
| Total | 100 | 131 | 75 | 26 | 118 | 450 |

#### Relative Frequency Table (Partial):
| | To Fly | Freeze Time | Invisibility | Super Strength | Telepathy | Total |
|-----------|--------------|------------------|-------------------|---------------------|------------------|---------------|
| Females | $\frac{49}{450} \approx 0.109$ | | | | | $\frac{228}{450} \approx 0.507$ |
| Males | | | $\frac{27}{450} \approx 0.060$ | | | |
| Total | | $\frac{131}{450} \approx 0.291$ | | | $\frac{118}{450} \approx 0.262$ | |

Solution Approach:

To complete the relative frequency table, we will calculate the relative frequency for each cell by dividing the frequency of that cell by the total number of observations (450). We will then round the results to the nearest thousandth.

#### Step 1: Calculate Relative Frequencies for "Females" Row
- To Fly: Already calculated as $ \frac{49}{450} \approx 0.109 $.
- Freeze Time: $ \frac{60}{450} = 0.133 $.
- Invisibility: $ \frac{48}{450} = 0.107 $.
- Super Strength: $ \frac{1}{450} = 0.002 $.
- Telepathy: $ \frac{70}{450} = 0.156 $.

#### Step 2: Calculate Relative Frequencies for "Males" Row
- To Fly: $ \frac{51}{450} = 0.113 $.
- Freeze Time: $ \frac{71}{450} = 0.158 $.
- Invisibility: Already calculated as $ \frac{27}{450} \approx 0.060 $.
- Super Strength: $ \frac{25}{450} = 0.056 $.
- Telepathy: $ \frac{48}{450} = 0.107 $.

#### Step 3: Verify Totals
The totals for each row and column should sum up correctly when converted to relative frequencies. For example:
- Total for Females: $ 0.109 + 0.133 + 0.107 + 0.002 + 0.156 = 0.507 $.
- Total for Males: $ 0.113 + 0.158 + 0.060 + 0.056 + 0.107 = 0.494 $ (Note: Due to rounding, there might be a slight discrepancy).

Completed Relative Frequency Table:

| | To Fly | Freeze Time | Invisibility | Super Strength | Telepathy | Total |
|-----------|--------------|------------------|-------------------|---------------------|------------------|---------------|
| Females | $\frac{49}{450} \approx 0.109$ | $\frac{60}{450} \approx 0.133$ | $\frac{48}{450} \approx 0.107$ | $\frac{1}{450} \approx 0.002$ | $\frac{70}{450} \approx 0.156$ | $\frac{228}{450} \approx 0.507$ |
| Males | $\frac{51}{450} \approx 0.113$ | $\frac{71}{450} \approx 0.158$ | $\frac{27}{450} \approx 0.060$ | $\frac{25}{450} \approx 0.056$ | $\frac{48}{450} \approx 0.107$ | $\frac{222}{450} \approx 0.494$ |
| Total | $\frac{100}{450} \approx 0.222$ | $\frac{131}{450} \approx 0.291$ | $\frac{75}{450} \approx 0.167$ | $\frac{26}{450} \approx 0.058$ | $\frac{118}{450} \approx 0.262$ | $1.000$ |

Final Answer:

$$
\boxed{
\begin{array}{|c|c|c|c|c|c|c|}
\hline
& \text{To Fly} & \text{Freeze Time} & \text{Invisibility} & \text{Super Strength} & \text{Telepathy} & \text{Total} \\
\hline
\text{Females} & 0.109 & 0.133 & 0.107 & 0.002 & 0.156 & 0.507 \\
\hline
\text{Males} & 0.113 & 0.158 & 0.060 & 0.056 & 0.107 & 0.494 \\
\hline
\text{Total} & 0.222 & 0.291 & 0.167 & 0.058 & 0.262 & 1.000 \\
\hline
\end{array}
}
$$