Question

Find Mean Deviation from median of the marks secured by 100 students in a class-test as given below:

Marks	:	60-63	63-66	66-69	69-72	72-75
No. of Students	:	5	18	42	27	8

Answer 1

Marks	Mid Value	f	c.f	Deviation from Median DM = |m−M| (M= 67.93)	f|DM|
60−63	61.5	5	5	6.43	32.15
63−66	64.5	18	23	3.43	61.74
66−69	67.5	42	65	0 .43	18.06
69−72	70.5	27	92	2.57	69.39
72−75	73.5	8	100	5.57	44.56
		Σf = 100			Σf|DM| = 225.9

The median class is given by the size of the${\left(\frac{N}{2}\right)}^{\mathrm{th}}$item, i.e. the ${\left(\frac{100}{2}\right)}^{\mathrm{th}}$item, which is the 50^th item.
This corresponds to the class interval 66−69, so this is the median class.

$$\begin{gathered} M=l_1+\frac{{\displaystyle \frac{N}{2}-c.f}}{f}\times i \\ =66+\frac{50-23}{42}\times 3 \\ =66+1.93 \\ =67.93 \\ \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }f\left|D_M\right|}{\Sigma f}=\frac{225.9}{100}=2.259=2.26 \end{gathered}$$