Question

Find the mean deviation about the mean for the data:

Income per day	Numbers of persons
0-100	4
100-200	8
200-300	9
300-400	10
400-500	7
500-600	5
600-700	4
700-800	3

Answer 1

Income per day	Number of persons $\left(f_i\right)$	Mid-point $X_i$	$\left(f_i{X}_i\right)$	$|X_i-\overline{X}|$	$f_i|X_i-\overline{X}|$
0-100	4	50	200	308	1232
100-200	8	150	1200	208	1664
200-300	9	250	2250	108	972
300-400	10	350	3500	8	80
400-500	7	450	3150	92	644
500-600	5	550	2750	192	960
600-700	4	650	2600	292	1168
	50		17900		7896

Here $N=\sum _{i=1}^8{f}_i=50$

${\sum }_{i=1}^8{f}_1{x}_i=17900$
$\therefore \overline{X}=\frac{1}{N}\sum _{i=1}^8{f}_i{x}_i=\frac{1}{50}\times 17900=358$
$\therefore M.D.\left(\overline{x}\right)=\frac{1}{N}\sum _{i=1}^8{f}_i\mid x_1-\overline{x}\mid =\frac{1}{50}\times 7896=157.92$