1. The problem is to find the rank correlation coefficient for the given data sets. 2. The rank correlation coefficient formula (Spearman's rho) is: $$\rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)}$$ where $d_i$ is the difference between ranks of each pair and $n$ is the number of pairs. 3. From the data, ranks by A and B are: Rank by A: $[1, 6, 5, 10, 3, 2, 4, 9, 7, 8]$ Rank by B: $[3, 5, 8, 4, 7, 10, 2, 1, 6, 9]$ 4. Calculate differences $d_i = \text{Rank A}_i - \text{Rank B}_i$: $d = [1-3, 6-5, 5-8, 10-4, 3-7, 2-10, 4-2, 9-1, 7-6, 8-9] = [-2, 1, -3, 6, -4, -8, 2, 8, 1, -1]$ 5. Square each difference: $d^2 = [4, 1, 9, 36, 16, 64, 4, 64, 1, 1]$ 6. Sum of squared differences: $$\sum d_i^2 = 4 + 1 + 9 + 36 + 16 + 64 + 4 + 64 + 1 + 1 = 200$$ 7. Number of pairs $n = 10$ 8. Substitute into formula: $$\rho = 1 - \frac{6 \times 200}{10(10^2 - 1)} = 1 - \frac{1200}{10 \times 99} = 1 - \frac{1200}{990} = 1 - 1.2121 = -0.2121$$ 9. Interpretation: The rank correlation coefficient is approximately $-0.21$, indicating a weak negative correlation between the two rankings. Final answer: $$\boxed{\rho \approx -0.21}$$