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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Consider any set of observations $x_{1}, x_{2}, x_{3}, \ldots, x_{101}$ It is given that $x_{1}<\,x_{2}<\, x_{3}<\, \ldots<\, x_{100}<\, x_{101}$ ; 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 an item equidistant from the beginning and the end, i.e., the median. In this case, the median is $\frac{101+1}{2}$ th, i.e., 51 st item, i.e., $x_{51}$