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JEE Main202127 Aug 2021Morning ShiftMathematicsStatisticsActual

Let n be an odd natural number such that the variance of 1 , 2 , 3 , 4 , … , n is 14 . Then n is equal to ________.

Correct answer

0

Step-by-step solution

Variance of n natural number is given by, Variance = ∑ n 2 n - ∑ n n 2 = n n + 1 2 n + 1 6 n - n n + 1 2 n 2 = n + 1 2 n + 1 6 - n + 1 4 = n + 1 n - 1 12 = n 2 - 1 12 And it is given that Variance = 14 ⇒ n 2 - 1 12 = 14 ⇒ n 2 - 1 = 168 ⇒ n = 13

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