This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Option 2 : \(\dfrac{1}{12}m(m-1)(m+1)\)

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10 Questions
10 Marks
7 Mins

**Explanation**

According to Spearman's rank correlation coefficient when ranks are repeated is as follows -

⇒ r_{s} = 1 - 6[(∑d^{2} + (m_{1}^{3} - m_{1})/12 + (m_{2}^{3} - m_{2})/12 + -------)]/n(n^{2} - 1)

m_{1}, m_{2} ----- are the number of repetitions of the ranks

(m_{1}^{3} - m_{1})/12 ----- are corresponding factors

**∴ The factor is added for each repeating value in the both series is given by (m ^{3} - m)/12 = m(m^{2} - 1)/12 = m(m - 1)(m + 1)/12**

Originally the spearsman rank correlation is denotted by rs = 1-6∑d2/n(n^{2} - 1)