Question

Find the mean deviation about the mean for the data

Height of cms	Number of boys
95-105	9
105-115	13
115-125	26
125-135	30
135-145	12
145-155	10

Answer 1

The following table is formed

Height of cms	Number of boys$f_i$	mid-point $X_i$	$f_i\times X_i$	$\mid x_i-\overline{x}\mid$	$f_i\mid x_i-\overline{x}\mid$
95-105	9	100	900	25.3	227.7
105-115	13	110	1430	14.3	198.9
115-125	26	120	3120	5.3	137.8
125-135	30	130	3900	4.7	141
135-145	12	140	1680	14.7	176.4
145-155	10	150	1500	24.7	247

Here $N=\sum _{i=1}^6{f}_i=100,\sum _{i=1}^6{f}_1{x}_i=12530$
$\therefore \overline{X}=\frac{1}{N}\sum _{i=1}^6{f}_i{x}_i=\frac{1}{100}\times 12530=125.3$
$\therefore M.D.\left(\overline{x}\right)=\frac{1}{N}\sum _{i=1}^6{f}_i\mid x_1-\overline{x}\mid =\frac{1}{100}\times 1128.8=11.28$