Statistics And Probability Question 385
Question: 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
Options:
A) $ x_1 $
B) $ x_{51} $
C) $ \frac{x_1+x_2+…+x_{101}}{101} $
D) $ x_{50} $
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Answer:
Correct Answer: B
Solution:
[b] Mean deviation is minimum when it is considered about the item, equidistant from the beginning and end i.e. the median. In case median is $ \frac{101+1}{2} $ th i.e., 51st item i.e., $ x_{51}. $
BETA
