Mean Deviation about Median

Q. If standard deviation of $x_i,i=1,2,......,n$ is ${\sigma }_x$, then the standard deviation of $\frac{a{x}_i+b}{p}\forall a,b,p\in R,i=1,2,3,.....,n$, is

1. $\left|\frac{a}{p}\right|{\sigma }_x$
2. $\frac{p}{a}{\sigma }_x$
3. $\frac{p}{2a}{\sigma }_x$
4. $\left|\frac{p}{a}\right|{\sigma }_x$

Q.

Calculate mean deviation about mean and median for given observations {1, 1, 4, 2, 6, 100, 150, 200, 400}

1. 102.4, 93.55

2. 102.4, 92.54

3. 1024, 92.55

4. 103.4, 93.55

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

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

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. $x_1$

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

3. $x_{101}$

4. $x_{201}$

Q.

If the mean deviation about the median of the numbers $a,2a,......,50a$ is $50$, then $|a|$ equals

1. 3

2. 4

3. 5

4. 2

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 a point $k$ is minimum when $k$ equals

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

Q. The mean deviation about the median for the following data $3,7,8,9,4,6,8,13,12,10$ is:

1. $5.2$
2. $3.3$
3. $2.4$
4. $2$

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. 2.5

3. 2.9

4. 3

Q.

Calculate mean deviation about mean and median for given observations {1, 1, 4, 2, 6, 100, 150, 200, 400}

1. 103.4, 93.55

2. 102.4, 93.55

3. 1024, 92.55

4. 102.4, 92.54

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. $x_{201}$