Q. Consider any set of 201 observations$x_{1},x_{2},\ \ldots x_{200},x_{201}$. It is given that $x_{1} < x_{2} < \ldots < x_{200} < x_{201}$. Then, the mean deviation of this set of observations about a point $k$ is minimum when $k$ equals
A) $(x_{1} + x_{2} + ... + x_{200} + x_{201})/201$
B) $x_{1}$
C) $x_{101}$
D) $x_{201}$
Explanation
(c)
Given that, $x_{1} < x_{2} < x_{3} < \ldots < x_{201}$
$\therefore$ Median of the given observation $= \left( \frac{201 + 1}{2} \right)$th item Now, deviation will be minimum of taken from the median. $\therefore$ Mean deviation will be minimum, if $k = x_{101}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.