Question

Find the mean deviation from the median for the data: 

xi	74	89	42	54	91	94	35
fi	20	12	2	4	5	3	4

Answer 1

xi	fi	Cumulative Frequency	\[\left| x_i - 74 \right|\]	\[f_i \left| x_i - 74 \right|\]
35	4	4	39	156
42	2	6	32	64
54	4	10	20	80
74	20	30	0	0
89	12	42	15	180
91	5	47	17	85
94	3	50	20	60
	\[N = \Sigma f_i = 50\]	Total = 189		\[\sum^n_{i = 1} f_i \left| x_i - 74 \right| = 625\]

Here,

\[\frac{N}{2} = \frac{50}{2} = 25\]

The cumulative frequency greater than 25 is 30 and the corresponding value of x is 74.

\[\text{ Median}, M = 89\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - M \right| = \frac{1}{50} \times 625 = 12 . 5\].