Rank each judge's scores separately from highest to lowest, then apply Spearman's formula to the two rank columns.

Step 1 — Rank Judge A's scores. Scores $45,38,30,42,25$, sorted highest to lowest: $45>42>38>30>25$. So contestant 1 (45) gets rank 1, contestant 4 (42) rank 2, contestant 2 (38) rank 3, contestant 3 (30) rank 4, contestant 5 (25) rank 5.

Step 2 — Rank Judge B's scores. Scores $40,35,32,44,20$, sorted highest to lowest: $44>40>35>32>20$. So contestant 4 (44) gets rank 1, contestant 1 (40) rank 2, contestant 2 (35) rank 3, contestant 3 (32) rank 4, contestant 5 (20) rank 5.

Step 3 — Tabulate both rank columns and find $d, d^2$.

$\sum d^2 = 1+0+0+1+0=2$. (No ranks are tied on either list, so the standard formula applies directly.)

Step 4 — Apply the formula, $n=5$. …

Ranking a judge's scores from lowest to highest instead of highest to lowest (or being inconsistent between the two judges) inverts the whole calculation — always fix a single convention (here, rank 1 = highest score) and apply it to both judges identically. Forgetting to convert the raw scor …