Q.Two judges, A and B, ranked 5 contestants (P, Q, R, S, T) in a debate competition as follows — Judge A: 1, 2, 3, 4, 5; Judge B: 2, 1, 4, 3, 5 (for P, Q, R, S, T respectively). Calculate Spearman's Rank Correlation Coefficient and comment on the agreement between the judges.

Spearman's coefficient measures agreement between two rankings using the differences between corresponding ranks. …

Step 1 — Differences in ranks (d) for each contestant.

Step 2 — Apply the formula (n = 5):

$r_s = 1 - \frac{6\Sigma d^2}{n(n^2-1)} = 1 - \frac{6 \times 4}{5(25-1)} = 1 - \frac{24}{120} = 1 - 0.2 = 0.8$ …

Cross-check by applying Pearson's formula directly to the ranks (valid since there are no tied ranks): mean of A's ranks = 3, mean of B's ranks = 3; deviations of A: −2,−1,0,1,2; deviations of B: −1,−2,1,0,2; Σ(product) = 2+2+0+0+4 = 8; Σ(A-dev)² = 10; Σ(B-dev)² = 1+4+1+0+4 = …

Squaring d before summing rather than summing d first and then squaring the total (Σd² ≠ (Σd)²) — the formula strictly requires the sum of the INDIVIDUAL squared differences; also using n³−n instead of n(n²−1) is fine since th …