Calculate rank correlation between advertisement cost and sales as per the data given below:

Cost (in '000 ₹) 78 36 98 25 75 82 90 62 65 39

Sales (in lakh ₹) 84 51 91 60 68 62 86 58 53 47

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Solution

Advertising Cost
(X) Sales
(Y) R₁ R₂ D= R₁−R₂
D²

78
36
98
25
75
82
90
62
65
39 84
51
91
60
68
62
86
58
53
47 7
2
10
1
6
8
9
4
5
3 8
2
10
5
7
6
9
4
3
1 −1
0
0
−4
−1
2
0
0
2
2 1
0
0
16
1
4
0
0
4
4

$Σ D^{2}$ =30

N= 1

$r_{k} = 1 - \frac{6 Σ D^{2}}{N^{3} - N} or, r_{k} = 1 - \frac{6 \times 30}{1000 - 10} or, r_{k} = 1 - 0.1818 = - 0.818 \Rightarrow r_{k} = - 0.82$

Hence, coefficient of rank correlation = -0.82

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Cost (in '000 ₹)	78	36	98	25	75	82	90	62	65	39
Sales (in lakh ₹)	84	51	91	60	68	62	86	58	53	47