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

Monjur Alahi

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


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Correct Answer - B
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)`.

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