Question

Find the mean deviation about the mean for the data.

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

Answer 1

The following table is formed.

Income per day| Number of persons $f_i$| Mid-point $x_i$| $f_ix_i$| $|x_i-\bar{x}$| $f_i|x_i-\bar{x}$|
---|---|---|---|---|---
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
700-800| 3| 750| 2250| 392| 1176
| 50| | 17900| | 7896

Here, $\sum_{I=1}^{8}f_i=50\sum_{1=i}^8f_ix_i=17900$

∴ $\bar{x}=\frac{1}{N}\sum_{i=1}^{8}f_ix_i=\frac{1}{50}×17900=358$

$M.D(\bar{x})=\frac{1}{N}\sum_{i=1}^{8}f_i|x_i-\bar{x_i}|=\frac{1}{50}×7896=157.92$