# If the mean deviation of number $1,1+d,1+2d.........1+100d$  from their mean is 255, then the $d$ is equal to : Option 1) 20.0 Option 2) 10.1 Option 3) 20.2 Option 4) 10.0

G gaurav

As we have learnt,

Mean Deviation -

If x1, x2, ...xn are n observations then the mean deviation from the point A is given by :

$\dpi{100} \frac{1}{n}\sum \left | x_{i}-A \right |$

-

We have,

$255 = \frac{1}{101}\left (\sum_{i=0}^{101} (x_i - A) \right )$

Here,

$A = 1 + \frac{1}{101}\left(\frac{100\times 101}{2} \right )d = 1 + 50d$

$\\\therefore 255 = \frac{2(50d + 49d + ... + d)}{101} \\\Rightarrow d = \frac{255\times 101\times2}{2\times 50\times 51} = 10.1$

Option 1)

20.0

Option 2)

10.1

Option 3)

20.2

Option 4)

10.0

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