स्पीयरमैन श्रेणी में सहसंबंध गुणांक rs = 1 - \(\dfrac{6∑ d^2}{n(n^2-1)}\) है, संयुक्त श्रेणी के मामले में ∑d2 का अधिकतम मान है:

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SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. \(\dfrac{1}{2}(n^2 - 1)\)
  2. \(\dfrac{1}{4}n(n^2 - 1)\)
  3. n
  4. \(\dfrac{1}{3}n(n^2 - 1)\)

Answer (Detailed Solution Below)

Option 4 : \(\dfrac{1}{3}n(n^2 - 1)\)
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दिया गया है

संयुक्त श्रेणी के मामले में rका मान = -1

गणना

यहाँ, स्पीयरमैन श्रेणी सहसंबंध गुणांक rs = -1

⇒ 1 - \(\dfrac{6∑ d^2}{n(n^2-1)}\) = -1

⇒ \(\dfrac{6∑ d^2}{n(n^2-1)}\) = 2

⇒ 6 \(∑ \)d2 = 2n(n2 - 1)

⇒  Σd2 = n(n2 - 1)/3

संयुक्त श्रेणी के मामले में ∑dका अधिकतम मान है = \(\dfrac{1}{3}n(n^2 - 1)\)

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