1. **State the problem:** We are given a data set and asked to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. 2. **Organize the data:** The data set is already sorted: $$194, 226.2, 239.2, 257.1, 286, 297.8, 297.9, 319.6, 323.8, 340.1, 369.5, 378.3, 389.7, 389.7, 389.7, 394.8, 396, 396.6, 397.7, 402.2, 404.7, 410.6, 416.8, 427.8, 433.3, 450.2, 458.2, 458.2, 460.4, 462.3, 470, 471.3, 471.8, 475.1, 475.2, 477.2, 483.1, 488.8, 496.4, 498.4, 498.4, 498.4, 511.4, 539.6, 559.3, 581.3, 584.8, 606.2, 619.3, 652.3, 682.6, 700.1, 736.7, 737.5$$ 3. **Count the number of data points:** There are $n=52$ values. 4. **Find the minimum:** The smallest value is the first data point: $$\text{minimum} = 194$$ 5. **Find the maximum:** The largest value is the last data point: $$\text{maximum} = 737.5$$ 6. **Find the median:** Since $n=52$ is even, the median is the average of the 26th and 27th values. The 26th value is $450.2$ and the 27th value is $458.2$. Calculate median: $$\text{Median} = \frac{450.2 + 458.2}{2} = \frac{908.4}{2} = 454.2$$ 7. **Find the first quartile (Q1):** Q1 is the median of the lower half (first 26 values). The lower half has 26 values, so Q1 is the average of the 13th and 14th values. The 13th value is $389.7$ and the 14th value is $389.7$. Calculate Q1: $$Q_1 = \frac{389.7 + 389.7}{2} = 389.7$$ 8. **Find the third quartile (Q3):** Q3 is the median of the upper half (last 26 values). The upper half has 26 values, so Q3 is the average of the 13th and 14th values in this half, which correspond to the 39th and 40th values overall. The 39th value is $496.4$ and the 40th value is $498.4$. Calculate Q3: $$Q_3 = \frac{496.4 + 498.4}{2} = \frac{994.8}{2} = 497.4$$ **Final answers:** - Minimum = 194 - Q1 = 389.7 - Median = 454.2 - Q3 = 497.4 - Maximum = 737.5