In Spearman rank correlation coefficient rs = 1 - , the maximum value of ∑d2 in case of untied rank is:

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SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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Given

In the case of the untied rank maximum value of r= -1

Calculation

Here, Spearman rank correlation coefficient rs = -1

⇒ 1 -  = -1

⇒  = 2

⇒ 6 d2 = 2n(n2 - 1)

⇒  Σd2 = n(n2 - 1)/3

∴ The maximum value of ∑din case of untied rank is = 

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