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,  \(\sum_{I=1}^{8}f_i=50\sum_{1=i}^8f_ix_i=17900\)

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

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