Question

Find the mean deviation from the median for the  data:

xi	15	21	27	30	35
fi	3	5	6	7	8

 

Answer 1

xi	fi	Cumulative Frequency	\[\left| x_i - 30 \right|\]	\[f_i \left| x_i - 30 \right|\]
15	3	3	15	45
21	5	8	9	45
27	6	14	3	18
30	7	21	0	0
35	8	29	5	40
	\[N = \Sigma f_i = 29\]			\[\sum^n_{i = 1} f_i \left| x_i - 30 \right| = 148\]

Here, 

\[\frac{N}{2} = \frac{29}{2} = 14 . 5\]

The cumulative frequency greater than 14.5 is 21 and the corresponding value of x is 30.

\[\text{ Median, }  M = 30\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - M \right| = \frac{1}{29} \times 148 = 5 . 10\]