1. **Problem Statement:** Calculate Spearman's rank correlation coefficient for the given ranks of seven students in Statistics and Economics. 2. **Formula:** Spearman's rank correlation coefficient $\rho$ is given by: $$\rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}$$ where $d_i$ is the difference between the ranks of each student in the two subjects, and $n$ is the number of students. 3. **Step 1: List the ranks and calculate differences $d_i$:** \begin{align*} \text{Student} & : A & B & C & D & E & F & G \\ \text{Statistics} & : 2 & 1 & 4 & 3 & 5 & 7 & 6 \\ \text{Economics} & : 1 & 3 & 2 & 4 & 5 & 6 & 7 \\ \text{Difference } d_i & : 2-1=1 & 1-3=-2 & 4-2=2 & 3-4=-1 & 5-5=0 & 7-6=1 & 6-7=-1 \end{align*} 4. **Step 2: Calculate $d_i^2$ for each student:** $$d_i^2 = 1^2, (-2)^2, 2^2, (-1)^2, 0^2, 1^2, (-1)^2 = 1, 4, 4, 1, 0, 1, 1$$ 5. **Step 3: Sum of squared differences:** $$\sum d_i^2 = 1 + 4 + 4 + 1 + 0 + 1 + 1 = 12$$ 6. **Step 4: Calculate $\rho$ using $n=7$:** $$\rho = 1 - \frac{6 \times 12}{7(7^2 - 1)} = 1 - \frac{72}{7(49 - 1)} = 1 - \frac{72}{7 \times 48} = 1 - \frac{72}{336} = 1 - 0.2143 = 0.7857$$ 7. **Final answer:** Spearman's rank correlation coefficient is approximately $0.786$. This indicates a strong positive correlation between the students' ranks in Statistics and Economics.