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JEE Main202124 Feb 2021Evening ShiftMathematicsStatisticsActual

If the variance of 10 natural numbers 1 , 1 , 1 , … , 1 , k is less than 10 , then the maximum possible value of k is ___________.

Correct answer

0

Step-by-step solution

σ 2 = Σ x 2 n - Σ x n 2 = 9 + k 2 10 - 9 + k 10 2 < 10 90 + 10 k 2 - 81 - k 2 - 18 k < 1000 9 k 2 - 18 k - 991 < 0 k 2 - 2 k < 991 9 k - 1 2 < 1000 9 - 10 10 3 < k - 1 < 10 10 3 k < 10 10 3 + 1 k ≤ 11 Maximum value of k is 11 .

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