What is the rank correlation coefficient of the following data ? x_i 1 2 3 4 5 6 7 y_i 2 3 5 6 8 7 8

Correct Answer is : None of the above

TS ICET 2017 Question Paper with Solutions for online practice

Question : 146 of 200

Marks: +1, -0

What is the rank correlation coefficient of the following data ?

$x_i$	1	2	3	4	5	6	7
$y_i$	2	3	5	6	8	7	8

Solution:

$x_i$	$y_i$	Rank of x (x)	Rank of y (y)	$d_i(x-y)$	$d_i^2$
1	2	1	1	0	0
2	3	2	2	0	0
3	5	3	3	0	0
4	6	4	4	0	0
5	8	5	6.5	-1.5	2.25
6	7	6	5	1	1
7	8	7	6.5	0.5	0.25

Here ,

n=7

Σd_i^2=3.5

Since 8 is repeated twice in column

y_i

,
Correction factor (C.F.)

={2(2^2-1)}/12={2×3}/12=0.5

∴ Rank correlation coefficient

=1-{6(Σd_i^2+C.F)}/{n(n^2-1)}

=1-{6×(3.5+0.5)}/{7(7^{2}-1)}=1-{6×4}/{7×48}=1-{1}/{14}={13}/{14}

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