1. **Problem Statement:** Calculate Spearman's rank correlation coefficient to assess the consistency between employee performance scores and peer review rankings. 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 pair and $n$ is the number of pairs. 3. **Step 1: Assign ranks to Performance Scores:** Performance Scores: 90, 76, 84, 70, 88, 82 Ranks (highest score rank 1): - 90: 1 - 88: 2 - 84: 3 - 82: 4 - 76: 5 - 70: 6 4. **Step 2: Given Peer Review Ranks:** 1, 3, 2, 6, 4, 5 5. **Step 3: Calculate differences $d_i$ and $d_i^2$:** | Employee | Performance Rank | Peer Review Rank | $d_i$ = Perf Rank - Peer Rank | $d_i^2$ | |----------|------------------|------------------|------------------------------|---------| | 1 | 1 | 1 | 0 | 0 | | 2 | 5 | 3 | 2 | 4 | | 3 | 3 | 2 | 1 | 1 | | 4 | 6 | 6 | 0 | 0 | | 5 | 2 | 4 | -2 | 4 | | 6 | 4 | 5 | -1 | 1 | Sum of $d_i^2 = 0 + 4 + 1 + 0 + 4 + 1 = 10$ 6. **Step 4: Calculate $\rho$:** Number of pairs $n = 6$ $$\rho = 1 - \frac{6 \times 10}{6(6^2 - 1)} = 1 - \frac{60}{6(36 - 1)} = 1 - \frac{60}{6 \times 35} = 1 - \frac{60}{210} = 1 - \frac{2}{7} = \frac{5}{7} \approx 0.714$$ 7. **Interpretation:** A Spearman's rank correlation coefficient of approximately 0.714 indicates a strong positive correlation between performance scores and peer review rankings, suggesting good consistency. Final answer: $\boxed{0.714}$