Question

Calculate mean deviation from the median of the following data: [NCERT EXEMPLAR]

Class interval:	0–6	6–12	12–18	18–24	24–30
Frequency	4	5	3	6	2

Answer 1

Calculation of mean deviation about the median.

Class Interval	Mid-Values (xi)	Frequency (fi)	Cummulative Frequency (c.f.)	$\left|x_i-14\right|$	$f_i\left|x_i-14\right|$
0–6	3	4	4	11	44
6–12	9	5	9	5	25
12–18	15	3	12	1	3
18–24	21	6	18	7	42
24–30	27	2	20	13	26
		N = 20			$\sum _{}{f}_i\left|x_i-14\right|=140$

Here, N = 20. So, $\frac{N}{2}=10$

The cummulative frequency just greater than $\frac{N}{2}$ is 12. Thus, 12–18 is the median class.

Now, l = 12, h = 6, f = 3 and F = 9

$\therefore \mathrm{Median}=l+\frac{{\displaystyle \frac{N}{2}}-F}{f}\times h=12+\left(\frac{10-9}{3}\right)\times 6=14$

Now,

Mean deviation about median = $\frac{1}{N}\sum _{}{f}_i\left|x_i-14\right|=\frac{1}{20}\times 140=7$