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  • Can someone explain If the mean deviation of the numbers 1, 1+d, ..., 1+100 d from their mean is 255, then a value of d is :

If the mean deviation of the numbers 1, 1+d, ..., 1+100 d from their mean is 255, then a value of d is :

  • Option 1)

    10.1

  • Option 2)

    20.2

  • Option 3)

    10

  • Option 4)

    5.05

     

 

Answers (1)

best_answer

As we learnt in 

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 |

-

 

mean=\frac{1+1+d+1+2d+----------1+100d}{101}=1+50d

Mean deviation

\Rightarrow \frac{1}{101}\sum_{r=0}^{100}\left | (I+rd) -(I+50d)\right |

\Rightarrow\frac{1}{101}\times 2d\times\frac{50\times51}{2}=255

d=10.1

 


Option 1)

10.1

This is correct option

Option 2)

20.2

This is incorrect option

Option 3)

10

This is incorrect option

Option 4)

5.05

 

This is incorrect option

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