1. **State the problem:** We need to find the median from an ungrouped frequency table with times and their corresponding frequencies. 2. **Given data:** Time (seconds): 4, 5, 6 Frequency: 4, 1, 5 3. **Formula and concept:** The median is the middle value when all data points are arranged in order. For frequency data, first find the total number of observations $N = \sum f_i$. 4. **Calculate total frequency:** $$N = 4 + 1 + 5 = 10$$ 5. **Find the median position:** Since $N=10$ (even), the median is the average of the $\frac{N}{2}$th and $\left(\frac{N}{2} + 1\right)$th values. So median position is between the 5th and 6th data points. 6. **Construct cumulative frequency table:** - For time 4: cumulative frequency = 4 - For time 5: cumulative frequency = 4 + 1 = 5 - For time 6: cumulative frequency = 5 + 5 = 10 7. **Locate median class:** The 5th data point corresponds to time 5 (since cumulative frequency reaches 5 at time 5). The 6th data point corresponds to time 6 (since cumulative frequency jumps to 10 at time 6). 8. **Calculate median:** Median = average of 5th and 6th values = $\frac{5 + 6}{2} = \frac{11}{2} = 5.5$ **Final answer:** The median time is $5.5$ seconds.