Question

Find the mean deviation from the mean for the data:

Classes	95-105	105-115	115-125	125-135	135-145	145-155
Frequencies	9	13	16	26	30	12

 

Answer 1

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

Classes	Frequency  \[f_i\]	Midpoints \[x_i\]	\[f_i x_i\]	\[\left| x_i - X \right|\] = \[\left| x_i - 128 . 58 \right|\]	\[f_i \left| x_i - X \right|\]
95−105	9	100	900	28.58	257.22
105−115	13	110	1430	18.58	241.54
115−125	16	120	1920	8.58	137.28
125−135	26	130	3380	1.42	36.92
135−145	30	140	4200	11.42	342.6
145−155	12	150	1800	21.42	257.04
	\[\sum^6_{i = 1} f_i = 106\]		\[\sum^6_{i = 1} f_i x_i = 13630\]		\[\sum^8_{i = 1}|  f_i x_i  |- \bar{x}= 1272.6\]

 

\[N = \sum^6_{i = 1} f_i = 106\] and

\[\sum^6_{i = 1} f_i x_i = 13630\]

\[\therefore X = \frac{\sum^6_{i = 1} f_i x_i}{\sum^6_{i = 1} f_i}\]

\[ = \frac{13630}{106}\]

\[ = 128 . 58\]

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

\[ = \frac{1272 . 6}{106}\]

\[ = 12 . 005\]