NIMCET 2019 Question Paper with solutions

Question : 18 of 120

Marks: +1, -0

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

Solution:

\ov{x}=\;\;{1+1+d+1+2d+. . .1+100d}/{101}

\ov{x}=\;\;{101}/{2}\;\;{(1+1+100d)}/{101}=1+150d

[|1-1-50d|+|1+d-1-50d|]

(\ov{x})=\;\;{+. . .+|1+100d-1-50d|]}/{101}

255=\;\;{2(50d+49d+. . .+2d+d)}/{101}

255=\;\;{2×d×50×51}/{2×101}

d=\;\;{255×101}/{50×51}=\;\;{101}/{10}=101

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