JEE Main202622 January 2026Evening ShiftMathematicsStatisticsActual

If the mean deviation about the median of the numbers k , 2 k , 3 k , . ., 1000 k is 500, then k ² is equal to :

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Correct answer

C. 4

Step-by-step solution

The sequence k, 2k, 3k, , 1000k has 1000 terms. The median is 500k + 501k 2 = 1001k 2 . The mean deviation is MD = 1 1000 _ i=1 ¹⁰⁰⁰|ik - median | . For i 500 : deviation = 1001k 2 - ik , giving _ i=1 ⁵⁰⁰( 1001 2 - i) = 125000 . By symmetry, the sum for i 501 is also 125000 . Thus MD = k 1000 250000 = 250k = 500 , so k = 2 and k^2 = 4 .

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