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 $\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

$x_i$	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
	$N=\Sigma f_i=197$			$\sum _{i=1}^n{f}_i\left|d_i\right|=336$

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.

$MD=\frac{1}{N}\sum _{i=1}^n{f}_i\left|d_i\right|=\frac{1}{197}\times 336=1.7055$