Mean Deviation about Median for Discrete Frequency Distributions

Q. Consider the following frequency distribution:
$\begin{array}{cccccc}\text{Class:}& 0-6& 6-12& 12-18& 18-24& 24-30\\ \text{Frequency :}& a& b& 12& 9& 5\end{array}$
If mean $=\frac{309}{22}$ and median $=14,$ then the value $(a-b{)}^2$ is equal to

Q. Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21

1. 6.53
2. 5.27
3. 12.96
4. 10.56

Q.

The mean deviation about the median for the following data

$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 6& 8& 14& 16& 4& 2\end{array}$

is

1. $9.35$
2. $10.34$
3. $11.35$
4. $12.33$

Q.

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

$\begin{array}{cccccccccc}\text{Heights in inches}& 58& 59& 60& 61& 62& 63& 64& 65& 66\\ \text{No. of students}& 15& 20& 32& 35& 22& 20& 10& 8& \end{array}$

Q. $d_i$ is the deviation of a class mark $y_i$ from ‘a’ the assumed mean and $f_i$ is the frequency, if $M_g=x+\frac{1}{\sum f_i}(\sum f_i{d}_i)$ , then x is

1. Class size
2. Number of observations
3. Lower limit
4. Assumed mean

Q. The mean deviation about the median for the following data
$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 6& 8& 14& 16& 4& 2\end{array}$
is

1. $9.35$
2. $10.34$
3. $11.35$
4. $12.33$

Q.

Calculate the mean deviation about median for the following data

$\begin{array}{cccccc}{X}_i& 3& 9& 10& 12& 13\\ f_i& 3& 4& 5& 2& 4\end{array}$

1. 2.21

2. 2.27

3. 2.56

4. 2.43

Q. Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21

1. 6.53
2. 5.27
3. 10.56
4. 12.96

Q. Calculate mean deviation from median for the following:

Marks (less than)	80	70	60	50	40	30	20	10
No. of Students	100	90	80	60	32	20	13	5

Q.

Calculate the mean deviation about median for the following data

$\begin{array}{cccccc}{X}_i& 3& 9& 10& 12& 13\\ f_i& 3& 4& 5& 2& 4\end{array}$

1. 2.21

2. 2.27

3. 2.56

4. 2.43

Q. For $(2n+1)$ observation $x_1,-x_1,x_2,-x_2,.....x_n,-x_n$ and $0$, where ${x_i}^8$ are distinct, non-zero numbers. Let S.D. and M.D. denote the standard deviation and median respectively. then, which one of the following is always true?

1. S.D.
2. S.D.$=$M.D.
3. S.D.>M.D.
4. Nothing can be said in general about the relationship of S.D. and M.D.

Q.

Read the following bar graph and fill in the blanks:

The mean strength of class IX and X is______.

Q.

Read the following bar graph and fill in the blanks:

The mean strength of classes VII, IX and X is______.

Q. The scores of $10$ students in a class test are given as $44,54,46,63,55,42,34,48,70,38$. Calculate the mean deviation about the median.

1. $8.6$
2. $6.6$
3. $7.6$
4. $8.8$
5. $Noneofthese$