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Question

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

A
20
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B
10.1
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C
20.2
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D
10
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Solution

The correct option is B 10.1
Mean =101+d(1+2+3++100)101
=1+d×100×101101×2=1+50d
Mean deviation from the mean =255
[|1(1+50d)|+|1+d(1+50d)|+|1+2d(1+50d)|++|1+100d(1+50d)|]101=255
2|d|[1+2+3+50]=101×255
2|d|×50×512=101×255
|d|=101×25550×51=10.1

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