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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

 

Answers (1)

best_answer

As we have learnt,

 

Mean Deviation -

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

\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

Posted by

gaurav

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