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JEE Main20199 Apr 2019Morning ShiftMathematicsStatisticsActual

If the standard deviation of the numbers - 1, 0 , 1 , k is 5 where k > 0 , then k is equal to

Options

  1. A6
  2. B4 5 3
  3. C2 10 3
  4. D2 6

Correct answer

D. 2 6

Step-by-step solution

S . D . = ∑ x i 2 n - ∑ x i n 2 = 5 ⇒ ∑ x i 2 n - ∑ x i n 2 = 5 ⇒ 1 + 1 + 0 + k 2 4 - - 1 + 0 + 1 + k 4 2 = 5 ⇒ 2 + k 2 4 - k 2 16 = 5   ⇒ 8 + 4 k 2 - k 2 16 = 5 ⇒ 8 + 3 k 2 = 80 ⇒ 3 k 2 = 72   ⇒ k 2 = 24   ⇒ k = ± 2 6 Since, k > 0   ⇒ k = 2 6 .

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