Question

Calculate the mean deviation about the median for the following data.

Height (in cm)	95-- 105	105- 115	115- 125	125- 135	135- 145	145- 155
Number of boys	9	13	25	30	13	10

• A. $17.34$
• B. $12.34$
• C. $15.33$
• D. $11.34$

Answer 1

Answer: (D)

First we find the median

Class	Frequency $f_i$	Cumulative Frequency $(C)$	Midvalue $(x_i)$
95 - 105	9	9	100
105-115	13	22	110
115-125	25	47	120
125-135	30	77	130
135 - 145	13	90	140
145 -155	10	100	150
	$N=\Sigma f_i=100$

Thus $N=100$ and therefore, $\frac{N}{2}=50$
$\Rightarrow$ median class is $125-135$.
$\Rightarrow l=125$, $f=30$, $h=10$ and $C=47$
$\therefore$ Median $=l+\frac{\left(\frac{N}{2}-C\right)}{f}\times h$
$=\left\{125+\frac{\left(50-47\right)}{30}\times 10\right\}=126$
$\therefore M=126$.
Now, we prepare the table given below.

$f_i$	$x_i$	$|x_i-M|$	$f_i|x_i-M|$
9	100	26	234
13	110	16	208
25	120	6	15
30	130	4	120
13	140	14	182
10	150	24	240
N=100			1134

$\therefore M.D.\left(M\right)=\frac{\Sigma f_i|x_i-M|}{N}$
$=\frac{1134}{100}=11.34$.