Question

Find the mean deviation from the mean for the data:

Classes	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800
Frequencies	4	8	9	10	7	5	4	3

 

Answer 1

  We will compute the mean deviation from the mean in the following way:  

Classes	\[f_i\]	Midpoints   \[x_i\]	\[f_i x_i\]	\[\left| x_i - X \right|\] =   \[\left| x_i - 358 \right|\]	\[f_i \left| x_i - X \right|\]
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
	\[\sum^8_{i = 1} f_i = 50\]		\[\sum^8_{i = 1} f_ix_i= 17900\]		\[\sum^8_{i = 1} f_i \left| x_i - X \right| = 7896\]

 

 

\[N = \sum^6_{i = 1} f_i = 50\] and 

\[\sum^6_{i = 1} f_i x_i = 17900\]

\[\bar{ X }  = \frac{\sum^{8} _{i = 1} f_i x_i}{\sum ^8_{i = 1} f_i} = \frac{17900}{50} = 358\]

\[\therefore \text{ Mean deviation } = \frac{1}{N} \sum^8_{i = 1} f_i \left| x_i - X \right|\]
\[ = \frac{7896}{50}\]
\[ = 157 . 92\]