Mean Deviation about Median

Q.

Consider any set of 201 observations $x_1,x_2,\cdots ,x_{200},x_{201}$. It is given that $x_1<x_2<\cdots <x_{200}<x_{201}$. Then, the mean deviation of this set of observations about a point k is minimum, when k equals

1. $\frac{x_1+x_2+\cdots +x_{200}+x_{201}}{201}$

2. $x_1$

3. $x_{101}$

4. $x_{201}$

Q.

Number of goals scored by Messi in champion's league for past 10 years is a follows: {1, 1, 6, 9, 8, 12, 14, 8, 8, 10}. Find the mean deviation about median.

1. 2.8

2. 2.9

3. 2.5

4. 3

Q. Consider set of observations $x_1,x_2,x_3,\cdots ,x_{101}$. It is given that $x_1<x_2<x_3\cdots <x_{100}<x_{101}$, then the mean deviation of the set of observations about $k$ is minimum when $k$ equals

1. $x_1$
2. $x_{51}$
3. $\frac{x_1+x_2+\cdots +x_{101}}{101}$
4. $\frac{x_{50}+x_{51}}{2}$

Q. The mean deviation of 2, 4, 6, 8, 10 about its mean is

1. 4.2
2. 2.4
3. 3.4
4. 4.3