NTA Abhyas JEE Main2020MathematicsStatisticsPractice

If the variance of first n even natural numbers is 133 , then the value of n is equal to

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Correct answer

D. 20

Step-by-step solution

V a r 2,4 , 6 . . . . . . . . . 2 n = 133 ⇒ 4 V a r 1,2 , 3 . . . . . . . . . n = 13 3 ⇒ V a r 1,2 , 3 . . . . . . . . . n = 133 4 ⇒ 1 2 + 2 2 + . . . . . . . n 2 n - 1 + 2 + 3 + . . . . . . . n n 2 = 133 4 ⇒ n + 1 2 n + 1 6 - n + 1 2 4 = 133 4 ⇒ n + 1 2 2 n + 1 3 - n + 1 2 = 133 4 ⇒ n + 1 2 n - 1 6 = 133 4 ⇒ n 2 - 1 = 399 ⇒ n = 2 0

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