यदि आवृत्ति वितरण का पहला, पाँचवाँ और नौवाँ दशमक क्रमशः 3, 10, 16 हैं, तो कैली का वैषम्य गुणांक क्या है?

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. \(-\frac{4}{13}\)
  2. \(-\frac{2}{13}\)
  3. \(-\frac{1}{13}\)
  4. \(-\frac{3}{13}\)

Answer (Detailed Solution Below)

Option 3 : \(-\frac{1}{13}\)
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Detailed Solution

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केली के वैषम्य गुणांक की गणना निम्नानुसार की जा सकती है:

\(D_9 = 16 (9th decile)\\ D_5 = 10 (5th decile)\\ D_1 = 3 (1st decile)\\ SK_k = \frac{(D_9 - 2D_5 +D_1)}{(D_9 - D1)}\\ SK_k = \frac{(16 - 2 * 10 + 3)}{(16 - 3)}\\ SK_k = \frac{(-1)}{13} \)

इस प्रकार, सही उत्तर \(\frac{-1}{3}\) है।

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