WAEC 2022 · Paper 2 · Q6

Vocal ( $X$ )	63	69	72	59	82	91	95	68
Instrumental ( $Y$ )	58	61	67	51	53	79	92	57

The table shows the scores obtained by a group of artistes in Vocal ( $X$ ) and Instrumental ( $Y$ ) musical competition.

(a)
Calculate the Spearman's rank correlation coefficient between the scores (3 d.p.).

Worked solution (try it first)

Rank the Vocal scores (1 for the highest): $7, 5, 4, 8, 3, 2, 1, 6$ .
Rank the Instrumental scores: $5, 4, 3, 8, 7, 2, 1, 6$ .
$d$ : $2, 1, 1, 0, -4, 0, 0, 0$ , so $\sum d^2 = 4 + 1 + 1 + 16 = 22$ .
$\rho = 1 - \dfrac{6 \times 22}{8 \times 63}$
$= 1 - \dfrac{132}{504}$
$= \dfrac{31}{42}$
$\approx 0.738$ .