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

Options

A. `10.0`
B. `20.0`
C. 10.1
D. 20.2

Answer

C

Explanation

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`