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If the mean deviation about the median of the numbers a,2a,........,50a\; is\; 50,then\; \left | a \right |\; equals

  • Option 1)

    4

  • Option 2)

    5

  • Option 3)

    2

  • Option 4)

    3

 

Answers (1)

best_answer

As we learnt in 

MEDIAN -

For discrete data:

in case of discrete data let x1,x2,x3......xn 

If the number of observations(n) is odd then the median is the value \left (\frac{n+1}{2} \right )^{th}observations after the observations are arranged in ascending or descending order of magnitude.

If n is even  then \left (\frac{n}{2} \right )^{th}and \left (\frac{n}{2} +1 \right )^{th}observations.

-

 

 and

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 |

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 Median of a,2a,3a,.....................50 \: \: is\:255

i.e. \frac{25a+26a}{2}=\frac{51a}{2}

Mean Deviation about=\frac{\left | \left(\frac{49}{2}a+\frac{47}{2}a+....................\frac{a}{2} \right )\times 2 \right |}{50}

=\frac{\left | a \right |(1+3+5+.....49)}{50}

=\left | a \right |\times\frac{ (625)}{50}=50   (given)

Thus \left | a \right | =\:4


Option 1)

4

Correct

Option 2)

5

Incorrect

Option 3)

2

Incorrect

Option 4)

3

Incorrect

Posted by

divya.saini

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