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Consider any set of observations $x_{1}, x_{2}, x_{3}, \dots, x_{101}$ . It is given that $x_{1} < x_{2} < x_{3} < \dots < x_{100} < x_{101}$ ; then the mean deviation of this set of observations about a point k is minimum when k equals

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x51

x1+x2+⋯+x101101

x50

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detailed solution

Correct option is 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+12 th, i.e., 51 st item, i.e., x51.

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Consider any set of observations x1,x2,x3,…,x101. It is 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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Consider any set of observations $x_{1}, x_{2}, x_{3}, \dots, x_{101}$ . It is given that $x_{1} < x_{2} < x_{3} < \dots < x_{100} < x_{101}$ ; then the mean deviation of this set of observations about a point k is minimum when k equals