Question

Calculate mean deviation and coefficient of mean deviation with the help of median:

Class Interval	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	15	19	14	20	18	14

Answer 1

x	Mid Value (m)	f	c.f.	|m−M| = |dM|	f|dM|
0 − 10 10 − 20 20 − 30	5 15 25	15 19 14	15 34 $\boxed{48}$	26 16 6	390 304 80
$\boxed{30}-40$	35	$\boxed{20}$	68	4	252
40 − 50 50 − 60	45 55	18 14	86 100	4 14	252 336
		∑fx = 100			∑f|dM| = 1446

Here, N or ∑fx = 100
Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{100}{2}\right)}^{th}$ item, which is 50^th item.
This corresponds to the class interval of 30 − 40, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=30+\frac{{\displaystyle \frac{100}{2}}-48}{20}\times 10 \\ \mathrm{or},\mathrm{Median}=30+\frac{2}{20}\times 10 \\ \mathrm{or},\mathrm{Median}=30+1 \\ \mathrm{Therefore},\mathrm{Median}=31 \end{gathered}$$

Thus, we calculate the deviation of values from 31.
$$\begin{gathered} \mathrm{Mean}\mathrm{Deviation}\mathrm{from}\mathrm{median}=\left(M{D}_M\right)=\frac{{\sum }_{}f\left|d_M\right|}{{\sum }_{}f}=\frac{1446}{100}=14.46 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Mean}\mathrm{Deviation}=\frac{\mathrm{Mean}\mathrm{Deviation}}{\mathrm{Median}}=\frac{14.46}{31}=0.466 \end{gathered}$$