Question

Find the mean deviation from the median for the following data:
(i)

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

(ii)

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

Answer 1

​i)

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
	$N=\Sigma f_i=29$			$\sum _{i=1}^n{f}_i\left|x_i-30\right|=148$

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.
$Median,M=30$
$MD=\frac{1}{N}\sum _{i=1}^n{f}_i\left|x_i-M\right|=\frac{1}{29}\times 148=5.10$

ii)

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
	$N=\Sigma f_i=50$			$\sum _{i=1}^n{f}_i\left|x_i-74\right|=625$

Here, $\frac{N}{2}=\frac{50}{2}=25$

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

$Median,M=89$

$MD=\frac{1}{N}\sum _{i=1}^n{f}_i\left|x_i-M\right|=\frac{1}{50}\times 775=12.5$