Explanation
Physics(P)
Mathematics (M)
Rank (P)
|d|
d2
48
60
72
62
56
40
39
52
30
78
65
70
38
54
32
31
6
3
1
2
4
7
8
5
9
0
n=9,∑d2=40
r=1−6∑d2n(n2−1)=1−40×69(92−1)=1−240720=0.66
Sl.No
Rank Difference (d)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
-2
-4
-1
16
∑d2=60,n=10
r=1−6∑d2n(n2−1)
r=1−6(60)10(102−1)
r=1−360990
r=0.6363....≈0.64
Students
History (H)
Mathematics(M)
Rank (H)
Rank(M)
A
B
C
D
E
F
G
H
I
J
K
L
69
36
71
67
76
20
85
55
34
33
25
79
22
83
81
24
35
46
64
10
12
11
49
100
n=12,∑d2=508
r=1−6∑d2n(n2−1)=1−6×50812(122−1)=1−30481716=−0.77
Since r<0, we can say that a very good student of history is a very bad student in mathematics.
Statistic (X)
Mathematics (Y)
XY
X2
Y2
15
80
∑X=56,∑Y=55,∑XY=369,∑X2=390,∑Y2=385
N=10
Cov(x,y)=∑XYN−∑XN.∑YN=36910−5610.5510=6.1
σx=√∑X2N−(∑X2N)2=√39010−(5610)2=2.76
σy=√∑Y2N−(∑Y2N)2=√38510−(5.5)2=2.87
r=Cov(x,y)σx.σy=6.12.87×2.76=0.77
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