calculate rank correlation and Karlpear sons method of correlation

x 77,54,27,52,14,35,90,25.56,60

y 35,58,60,46,50,40,35,56,44,42

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Question

calculate rank correlation and Karlpear sons method of
correlation
x 77,54,27,52,14,35,90,25 56,60
y 35,58,60,46,50,40,35,56,44,42

Prince Verma · Accepted Answer

Karl pearson's coefficient of correlation

x
y

dx(A=50)

dy(A=50)

(dx)â€‹2

(dy)â€‹2

dxdy

77
35
27
-15
729
225
-105

54
58
4
8
16
16
32

27
60
-23
10
529
100
-230

52
46
2
-4
4
16
-8

14
50
-36
0
1296
0
0

35
40
-15
-10
225
100
-150

90
35
40
-15
1600
225
-600

25
56
-25
6
625
36
-150

56
44
6
-6
36
36
-36

60
42
10
-8
100
64
-80

490
466
-10
-34
5160
818
-1319

r = ∑dxdy - ∑dx×dyN∑dx2-(∑dx)2n      ∑dy2-(∑dy)2n = -1319 - (-10)(-34)105160-(-10)210      818-(34)210 = -135371
7 ×26 5 = -13531900 05 = -0 71
Spearman's rank correlation

x
y
R
R
D
D2

77
35
2
9 5
-7 5
56 25

54
58
5
2
3
9

27
60
8
1
7
49

52
46
6
5
1
16

14
50
10
4
6
36

35
40
7
8
-1
1

90
35
1
9 5
-8 5
72 25

25
56
9
3
6
36

56
44
4
6
-2
4

60
42
3
7
-4
16

490
466

295 5

rk = 1 -6∑D2 - 112M13 - M1N3 - N= 1 - 6295
5 - 11223 - 2103 - 10= 1 - 1771990= 1-1
78=- 0 78

x	y	d_x(A=50)	d_y(A=50)	(d_x)²	(d_y)²	d_xd_y
77	35	27	-15	729	225	-105
54	58	4	8	16	16	32
27	60	-23	10	529	100	-230
52	46	2	-4	4	16	-8
14	50	-36	0	1296	0	0
35	40	-15	-10	225	100	-150
90	35	40	-15	1600	225	-600
25	56	-25	6	625	36	-150
56	44	6	-6	36	36	-36
60	42	10	-8	100	64	-80
490	466	-10	-34	5160	818	-1319

x	y	R	R	D	D²
77	35	2	9.5	-7.5	56.25
54	58	5	2	3	9
27	60	8	1	7	49
52	46	6	5	1	16
14	50	10	4	6	36
35	40	7	8	-1	1
90	35	1	9.5	-8.5	72.25
25	56	9	3	6	36
56	44	4	6	-2	4
60	42	3	7	-4	16
490	466				295.5

calculate rank correlation and Karlpear sons method of correlation x 77,54,27,52,14,35,90,25.56,60 y 35,58,60,46,50,40,35,56,44,42

calculate rank correlation and Karlpear sons method of correlation

x 77,54,27,52,14,35,90,25.56,60

y 35,58,60,46,50,40,35,56,44,42