Question

Find the mean deviation from the mean for the data:

Classes	0-10	10-20	20-30	30-40	40-50	50-60
Frequencies	6	8	14	16	4	2

Answer 1

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

Classes	Frequency    \[f_i\]	Midpoints   \[x_i\]	\[f_i x_i\]	\[\left| x_i - X \right|\] =   \[\left| x_i - 358 \right|\]	\[f_i \left| x_i - X \right|\]
0−10	6	5	30	22	132
10−20	8	15	120	12	96
20−30	14	25	350	2	28
30−40	16	35	560	8	128
40−50	4	45	180	18	72
50−60	2	55	110	28	56
	\[\sum^6_{i = 1} f_i = 50\]		\[\sum^6_{i = 1} f_i = 50\]		\[\sum^8_{i = 1} f_i \left| x_i - X \right| = 512\]

 

 

\[N = \sum^6_{i = 1} f_i = 50\]  and

\[\sum^6_{i = 1} f_i x_i = 1350\]

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

\[ = \frac{1350}{50}\]

\[ = 27\]

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

\[ = \frac{512}{50}\]

\[ = 10 . 24\]