Formula

1. `r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

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Examples
1. Calculate Spearman's Rank Correlation Coefficient from the following Data

X	35	40	42	43	40	53	54	49	41	55
Y	102	101	97	98	38	101	97	92	95	95

Solution:

`x`	`y`	`Rx`	`Ry`	`d=Rx-Ry`	`d^2`
35	102	10	1	9	81
40	101	8.5	2.5	6	36
42	97	6	5.5	0.5	0.25
43	98	5	4	1	1
40	38	8.5	10	-1.5	2.25
53	101	3	2.5	0.5	0.25
54	97	2	5.5	-3.5	12.25
49	92	4	9	-5	25
41	95	7	7.5	-0.5	0.25
55	95	1	7.5	-6.5	42.25
---	---	---	---	---	---
--	--	--	--	--	200.5

`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

`=1 - (6 * 200.5)/(10 * (10^2 - 1))`

`=1 - (6 * 200.5)/(10 * (100 - 1))`

`=1 - 1203/990`

`=1 - 1.22`

`=-0.22`

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2. Calculate Spearman's Rank Correlation Coefficient from the following Data

X	42	43	40	53	54	49	41	55
Y	97	98	38	101	97	92	95	95

Solution:

`x`	`y`	`Rx`	`Ry`	`d=Rx-Ry`	`d^2`
42	97	6	3.5	2.5	6.25
43	98	5	2	3	9
40	38	8	8	0	0
53	101	3	1	2	4
54	97	2	3.5	-1.5	2.25
49	92	4	7	-3	9
41	95	7	5.5	1.5	2.25
55	95	1	5.5	-4.5	20.25
---	---	---	---	---	---
--	--	--	--	--	53

`r = 1 - (6 * sum d^2)/(n(n^2 - 1))`

`=1 - (6 * 53)/(8 * (8^2 - 1))`

`=1 - (6 * 53)/(8 * (64 - 1))`

`=1 - 318/504`

`=1 - 0.631`

`=0.369`

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