Consider any set of observations `x_(1),x_(2),x_(3),..,x_(101)`. It is given that `x_(1) lt x_(2) lt x_(3) lt .. lt x_(100) lt x_(101)`, then the mean deviation of this set of observations about a point k is minimum when k equals

Options

A. `x_(1)`
B. `x_(51)`
C. `(x_(1)+x_(2)+..+x_(101))/(101)`
D. `x_(50)`

Answer

B

Explanation

Mean deviation is minimum when it is considered about an item equidistant from the beginning and the end, i.e., the median. In this case, the median is `(101+1)/(2)` th, i.e., 51st item, i.e., `x_(51)`.