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 :
A.
$${x_1}$$
B.
$${x_{51}}$$
C.
$$\frac{{{x_1} + {x_2} + ...... + {x_{101}}}}{{101}}$$
D.
$${x_{50}}$$
Answer :
$${x_{51}}$$
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 $${\left( {\frac{{101 + 1}}{2}} \right)^{th}}$$ i.e. $${51^{st}}$$ item i.e., $${x_{51}}.$$
Releted MCQ Question on Statistics and Probability >> Statistics
Releted Question 1
Select the correct alternative in each of the following. Indicate your choice by the appropriate letter only.
Let $$S$$ be the standard deviation of $$n$$ observations. Each of the $$n$$ observations is multiplied by a constant $$c.$$ Then the standard deviation of the resulting number is
Consider any set of 201 observations $${x_1},{x_2},.....\,{x_{200}},\,{x_{201}}.$$ It is given that $${x_1}\, < \,{x_2}\, < \,.....\, < {x_{200}}\, < {x_{201}}.$$ Then the mean deviation of this set of observations about a point $$k$$ is minimum when $$k$$ equals
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?