Question

Calculate the mean deviation from the median of the following frequency distribution:

Heights in inches	58	59	60	61	62	63	64	65	66
No. of students	15	20	32	35	35	22	20	10	8

Answer 1

In order to find the mean deviation from the median, we will first have to calculate the median.
M is the value of  x  corresponding to the cumulative frequency just greater than or equal to \[\frac{N}{2}\] .

 

\[x_i\]	fi	Cumulative Frequency	\[\left| d_i \right| = \left| x_i - 61 \right|\]	\[f_i \left| d_i \right|\]
58	15	15	3	45
59	20	35	2	40
60	32	67	1	32
61	35	102	0	0
62	35	137	1	35
63	22	159	2	44
64	20	179	3	60
65	10	189	4	40
66	8	197	5	40
	\[N = \Sigma f_i = 197\]			\[\sum^n_{i = 1} f_i \left| d_i \right| = 336\]

Here,

\[\frac{N}{2} = \frac{197}{2} = 98 . 5\]

The cumulative frequency just greater than 98.5 is 102. The corresponding value of x is 61.
Therefore, the median is 61.

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right| = \frac{1}{197} \times 336 = 1 . 7055\]