1. **State the problem:** We need to find the 58th percentile (P58) of a sorted data set with $n=117$ values. 2. **Formula for percentile position:** The position $L$ of the $k$th percentile in a sorted data set of size $n$ is given by: $$L = \frac{k}{100} \times (n + 1)$$ where $k=58$ and $n=117$. 3. **Calculate the position:** $$L = \frac{58}{100} \times (117 + 1) = 0.58 \times 118 = 68.44$$ 4. **Interpret the position:** The 58th percentile lies between the 68th and 69th data points. 5. **Find the 68th and 69th data values:** From the sorted data, - 68th value = 36.7 - 69th value = 36.8 6. **Interpolate to find P58:** $$P58 = x_{68} + (L - 68) \times (x_{69} - x_{68})$$ $$P58 = 36.7 + (68.44 - 68) \times (36.8 - 36.7)$$ $$P58 = 36.7 + 0.44 \times 0.1 = 36.7 + 0.044 = 36.744$$ 7. **Final answer:** The 58th percentile of the data set is approximately **36.744**.