Statistics And Probability Question 421
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
[DCE 1997]
Options:
A) $ x_1 $
B) $ x_{51} $
C) $ \frac{x_1+x_2+…+x_{101}}{101} $
D) $ x_{50} $
Show Answer
Answer:
Correct Answer: B
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} $ .
BETA
