Question

Consider any set of 201 observations $x_1,x_2,\cdots ,x_{200},x_{201}$. It is given that $x_1<x_2<\cdots <x_{200}<x_{201}$. Then, the mean deviation of this set of observations about a point k is minimum, when k equals

• A. $\frac{x_1+x_2+\cdots +x_{200}+x_{201}}{201}$
• B. $x_1$
• C. $x_{101}$
• D. $x_{201}$

Answer 1

The correct option is C

$x_{101}$

$x_1<x_2<x_3<\cdots <x_{201}$
$\therefore$ Median of the given observation $={\left(\frac{201+1}{2}\right)}^{\text{th}}$ item $=x_{101}$
Now, deviations will be minimum, if taken from the median.
$\therefore$ Mean deviation will be minimum, if k $=x_{101}$