Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a_1, a_2, a_3, \ldots, a_{100}$ is $25$. Then $S$ is

  • A
    $\phi$
  • B
    $\{99\}$
  • C
    $\mathbb{N}$
  • D
    $\{9\}$

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