Mean Deviation about Median

Q.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.

Daily Pocket Allowance(in c)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-35$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

Q.

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution :

$\begin{array}{ccccccccc}\text{Number of calls}& 0& 1& 2& 3& 4& 5& 6& 7\\ \text{Frequency}& 14& 21& 25& 43& 51& 40& 39& 12\end{array}$

Compute the mean deviation about median.

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. 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

Q.

The mean deviation from the median is

1. less than that measured from any other value.

2. equal to that measured from another values

3. maximum if all observations are positive

4. greater than that measured from any other value.

Q.

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19, and 20yr. One student is selected in such a manner that each has the same chance of being of chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and Standard Deviation (SD) of X.

Q.

The age distribution of 100 life insurance policy holders is as follows :

$\begin{array}{ccccccccc}\text{Age (on nearest birth day)}& 17-19.5& 20-25.5& 26-35.5& 36-40.5& 41-50.5& 51-55.5& 56-60.5& 61-70.5\\ \text{No. of persons}& 5& 16& 12& 26& 14& 12& 6& 5\end{array}$

Calculate the mean deviation from the median age.

Q.

Calculate the mean deviation about the median of the following frequency distribution :

$\begin{array}{cccccccc}{x}_i& 5& 7& 9& 11& 13& 15& 17\\ f_i& 2& 4& 6& 8& 10& 12& 8\end{array}$

Q.

Calculate the mean deviation about the median of the following observations :

(i) 3011, 2780, 3020, 2354, 3541, 4150, 5000

(ii) 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

(iii) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

(iv) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

(v) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

Q.

Calculate the mean deviation of the following income groups of five and seven members from their medians :

$\begin{array}{cc}\text{I}& \text{II}\\ \text{Income in Rs}& \text{Income in Rs}\\ 4000& 3800\\ 4200& 4000\\ 4400& 4200\\ 4600& 4400\\ 4800& 4600\\ & 4800\\ & 5800\end{array}$

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.

Find the value of $x,y$ and $z$ from the following equation:
(i) $\left[\begin{array}{cc}4& 3\\ x& 5\end{array}\right]=\left[\begin{array}{cc}y& z\\ 1& 5\end{array}\right]$

(ii) $\left[\begin{array}{cc}x+y& 2\\ 5+z& xy\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 5& 8\end{array}\right]$

(iii) $\left[\begin{array}{c}x+y+z\\ x+z\\ y+z\end{array}\right]=\left[\begin{array}{c}9\\ 5\\ 7\end{array}\right]$

Q.

Find the mean deviation from the median for the following data :

(i) $\begin{array}{cccccc}{x}_i& 15& 21& 27& 30& 35\\ f_i& 3& 5& 6& 7& 8\end{array}$

(ii) $\begin{array}{cccccccc}{x}_i& 74& 89& 42& 54& 91& 94& 35\\ f_i& 20& 12& 2& 4& 5& 3& 4\end{array}$

(iii) $\begin{array}{cccccc}\text{Marks obtained}& 10& 11& 12& 14& 15\\ \text{No. of students}& 2& 3& 8& 3& 4\end{array}$

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.

Calculate mean deviation about median age for the age distribution of 100 persons given below :

$\begin{array}{ccccccccc}\text{Age}& 16-20& 21-25& 26-30& 31-35& 36-40& 41-45& 46-50& 51-55\\ \text{No. of persons}& 5& 6& 12& 14& 26& 12& 16& 9\end{array}$

Q. Find the value of $a,b,c$ and $d$ from the equation:
$\left[\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right]=\left[\begin{array}{cc}-1& 5\\ 0& 13\end{array}\right]$

Q.

Compute the mean deviation from the median of the following distribution :

$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 5& 10& 20& 5& 10\end{array}$

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. $2.4$

Q. Find the mean deviation about the median for the data in the following:-
$x_i$ 5 7 9 10 12 15
$f_i$ 8 6 2 2 2 6

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. Number of terms free from radical sign in the expansion of ${(1+3^{1/3}+7^{1/2})}^{10}$ is

1. 4
2. 5
3. 6
4. 8

Q. If $a\ne p,b\ne q,c\ne r$ and $\left|\begin{array}{ccc}p& b& c\\ a& q& c\\ a& b& r\end{array}\right|$ = 0 then the value of $\frac{p}{p-a}+\frac{q}{q-b}+\frac{r}{r-c}$ is equal to

1. 2
2. 1
3. 3
4. c

Q. Distance between the two planes : $2x+3y+4z=4$ and $4x+6y+8z=12$ is

1. $2$ units
2. $4$ units
3. $8$ units
4. $\frac{2}{\sqrt{29}}$ units

Q. Mean deviation of $39,40,40,41,41,42,42,43,43,44,44,45$ from their median is?

1. $15$
2. $1.5$
3. $42$
4. $35$

Q. The mean deviation from the data $3,10,10,4,7,10,5$ is

1. $3$
2. $2$
3. $3.75$
4. $2.57$

Q. If the mean deviation about median for the number $3,5,7,2k,12,16,21,24$ arranged in the ascending order, is $6$ then the median is

1. $12$
2. $10.5$
3. $11.5$
4. $11$

Q. State True or False.

1. True
2. False

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. If $(b-c)x^2+(c-a)x+(a-b)=0$ has equal roots then $a,b,c$ are in :

1. A.P.
2. G.P.
3. H.P.
4. none

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