If the mean deviation of the numbers 1, 1+d, 1+2d,…,1+100d from their mean is 255, then d is equal to

If the mean deviation of the numbers 1, 1+d, 1+2d,...,1+100d from their mean is 255, then d is equal to

  1. A

    10.0

  2. B

    20.0

  3. C

    10.1

  4. D

    20.2

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    Solution:

    Let X denote the mean of the given numbers.

    Then,

      X¯=1+(1+d)+(1+2d)++(1+100d)101

     X¯=1012{1+(1+100d))101=1+50d

        Mean deviation =1101r=0100|(1+rd)(1+50d)|

       Mean deviation =1101r=0100|r50|

      Mean deviation =d101×2r=150r

      Mean deviation =2d101×50×512=50×51101d.

    It is given that the mean deviation is 255.

     255=50×51101dd=10.1

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