1. **Stating the problem:** We need to find the 75th percentile (P75) of the given data set: 70, 85, 90, 75, 80, 95, 85, 70, 80, 90. 2. **Sort the data in ascending order:** $$70, 70, 75, 80, 80, 85, 85, 90, 90, 95$$ 3. **Formula for percentile position:** $$P_k = \frac{k}{100} \times (n + 1)$$ where $k=75$ and $n=10$ (number of data points). 4. **Calculate the position:** $$P_{75} = \frac{75}{100} \times (10 + 1) = 0.75 \times 11 = 8.25$$ 5. **Interpret the position:** The 75th percentile lies between the 8th and 9th data points. 6. **Find the values at positions 8 and 9:** 8th value = 90 9th value = 90 7. **Calculate the 75th percentile by interpolation:** $$P_{75} = x_8 + 0.25 \times (x_9 - x_8) = 90 + 0.25 \times (90 - 90) = 90$$ 8. **Final answer:** The 75th percentile (P75) of the data is **90**.