The table shows the scores obtained by a group of artistes in Vocal (X) and the instrument (Y) musical competition. Vocal (X) 63 69 72 59 82 91 95 68 Instru...

Question 1 Report

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

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

Calculate the spearman's rank correlation coefficient between the scores.

Answer

p = $1 - \frac{6 Σ (d_{i})^{2}}{n (n^{2} - 1}$

p = Spearman's rank correlation coefficient
di = difference between the two ranks of each observation
n = number of observation

X	R $_{x}$	Y	R $_{y}$	D $_{I}$ (R $_{x}$ - R $_{y}$ )	D $_{i}$ $^{2}$
63	2	58	4	-2	4
69	4	61	5	-1	1
72	5	67	6	-1	1
59	1	51	1	0	0
82	6	53	2	4	16
91	7	79	7	0	0
95	8	92	8	0	0
68	3	57	3	0	0

P = $1 - \frac{6 (4 + 1 + 1 + 0 + 16 + 0 + 0 + 0)}{8 (8^{2} - 1)}$

p = $1 - \frac{6 (22)}{8 (63)}$

p = $1 - \frac{132}{504}$

p = $1 - \frac{11}{42}$

p = $\frac{11}{42}$

Read lesson note on Statistics (WAEC)

Answer Details

p = $1 - \frac{6 Σ (d_{i})^{2}}{n (n^{2} - 1}$

p = Spearman's rank correlation coefficient
di = difference between the two ranks of each observation
n = number of observation

X	R $_{x}$	Y	R $_{y}$	D $_{I}$ (R $_{x}$ - R $_{y}$ )	D $_{i}$ $^{2}$
63	2	58	4	-2	4
69	4	61	5	-1	1
72	5	67	6	-1	1
59	1	51	1	0	0
82	6	53	2	4	16
91	7	79	7	0	0
95	8	92	8	0	0
68	3	57	3	0	0

P = $1 - \frac{6 (4 + 1 + 1 + 0 + 16 + 0 + 0 + 0)}{8 (8^{2} - 1)}$

p = $1 - \frac{6 (22)}{8 (63)}$

p = $1 - \frac{132}{504}$

p = $1 - \frac{11}{42}$

p = $\frac{11}{42}$

Read lesson note on Statistics (WAEC)

View Answer