Question

Calculate the mean deviation about median for the following data.

Class	0- 10	10- 20	20- 30	30- 40	40- 50	50- 60
Frequency	6	7	15	16	4	2

• A. $10.16$
• B. $11.12$
• C. $12.16$
• D. $9.16$

Answer 1

Answer: (A)

Form the following table from the given data.

Class	Frequency $f_i$	Cumulative frequency $(c.f.)$	Mid points $x_i$	$|x_i-M|$	$f_i|x_i-M|$
0-10	6	6	5	23	138
10-20	7	13	15	13	91
20-30	15	28	25	3	45
30-40	16	44	35	7	112
40-50	4	48	45	17	68
50-60	2	50	55	27	54
	50				508

Here $N=50$
$\therefore \frac{N}{2}=25$
Therefore, $20-30$ is the median class.
Median $=l+\frac{\frac{N}{2}-C}{f}\times h$
Here $l=20$, $C=13$, $f=15$, $h=10$ and $N=50$
Therefore, Median $=20+\frac{25-13}{15}\times 10$
$=20+8=28$
Thus, Mean deviation about median is given by
$M.D.\left(M\right)=\frac{1}{N}\sum _{i=1}^6{f}_i\left|x_i-M\right|$
$=\frac{1}{50}\times 508=10.16$