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If the mean deviation of the numbers 1,"...

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

A

`10.0`

B

`20.0`

C

10.1

D

20.2

Text Solution

Verified by Experts

The correct Answer is:
C
Mean `(overline(x))=("sum of quantities")/(n)`
`=(n//2(a+1))/(n)=(1)/(2)[1+1+100d]`
=1+50d
`M.D. =(1)/(n) sum |x_(i)-overline(x)|`
`implies 25=(1)/(101)[50d+49d+48d+..+d+0+d..+50d]`
`=(2d)/(101)[(50xx51)/(2)]`
`implies d=(255xx101)/(50xx51)=10.1`
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