1. **State the problem:** We are given distances traveled by 19 employees and need to find the 25th and 50th percentiles (also known as the first quartile $Q_1$ and the median $Q_2$). 2. **Sort the data:** Arrange the distances in ascending order: $$0, 1, 3, 6, 7, 9, 9, 14, 14, 16, 18, 18, 20, 22, 24, 25, 28, 34, 36, 40$$ (Note: The user provided 19 values, but 20 are listed here; we will use the original 19 values: $$0, 1, 3, 6, 7, 9, 9, 14, 14, 16, 18, 18, 20, 22, 24, 25, 28, 34, 36$$) 3. **Formula for percentile position:** The position $P$ of the $k$th percentile in a sorted list of $n$ values is given by: $$P = \frac{k}{100} \times (n + 1)$$ 4. **Calculate the 25th percentile position:** $$P_{25} = \frac{25}{100} \times (19 + 1) = 0.25 \times 20 = 5$$ The 25th percentile is the value at the 5th position in the sorted list. 5. **Find the 25th percentile value:** The 5th value in the sorted list is $7$. 6. **Calculate the 50th percentile (median) position:** $$P_{50} = \frac{50}{100} \times (19 + 1) = 0.5 \times 20 = 10$$ The 50th percentile is the value at the 10th position. 7. **Find the 50th percentile value:** The 10th value in the sorted list is $16$. **Final answers:** - 25th percentile = $7$ - 50th percentile (median) = $16$