Question

6. The table shows the scores obtained by a group of artistes in Vocal (X) and Instrumental (Y) musical competition:
Vocal(x): 63,69,72,59,82,91,95,68
Instrumental(y): 58,61,67,51,53,79,92,57
Calculate the Spearman's rank correlation coefficient between the scores.

Accepted Answer

Ranking X and Y (1=lowest): R(X)=2,4,5,1,6,7,8,3 and R(Y)=4,5,6,1,2,7,8,3.
d=R(X)−R(Y): −2,−1,−1,0,4,0,0,0. d²: 4,1,1,0,16,0,0,0. Σd²=22.
Spearman's ρ = 1 − [6Σd²/(n(n²−1))] = 1 − [6(22)/(8×63)] = 1−0.2619 = 0.738 (moderate positive correlation).

WAEC Further Mathematics 2022 Theory — Question 6

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