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The mean deviation of the series a 2   ,   a 2 + d   ,   a 2 + 2 d ,   . . . . . ,   a 2 + 2 n d from its median is

Options

  1. An + 1 d 2 n + 1
  2. Bn d 2 n + 1
  3. Cn n + 1 d 2 n + 1
  4. D2 n + 1 d n n + 1

Correct answer

C. n n + 1 d 2 n + 1

Step-by-step solution

Median or mean x ¯ = 2 n + 1 2 ⋅ a 2 + a 2 + 2 n d 2 n + 1 = a 2 + n d ∵   M e a n = M e d i a n Σ x i - x ¯ = 2 d 1 + 2 + . . . . + n = n n + 1 d ∴   M . D . = n n + 1 d 2 n + 1

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