1. Tardigrade
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  4. Consider any set of observations x1, x2, x3, ...., x101; it being given that x1 < x2 < x3 < ... < x100 < x101 ; then the mean deviation of this set of observations about a point k is minimum when k equals

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Q. Consider any set of observations $x_1, x_2, x_3, ...., x_{101};$ it being given that $x_1 < x_2 < x_3 < ... < x_{100} < x_{101} ;$ then the mean deviation of this set of observations about a point k is minimum when k equals

Statistics

Solution:

Mean deviation is minimum when it is considered about the item, equidistant from the beginning and the end i.e. the median. In this case median is $\frac{101+1}{2} th$ i.e. 51st item i.e., $x_{51}$.