Question

Find the mean deviation about median for the following data

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of  Girls	6	8	14	16	4	2

Answer 1

The following table is formed.

Marks	Number of boys \(f_i\)	Cumulative frequency  \(c.f\)	Mid point \(x_i\)	\(|x_i-Med.|\)	\(f_i|x_i-Med.|\)
0-10	6	6	5	22.85	137.1
10-20	8	14	15	12.85	102.8
20-30	14	28	25	2.85	39.9
30-40	16	44	35	7.15	114.4
40-50	4	48	45	17.15	68.6
50-60	2	50	55	27.15	54.3
-	50	-	-	-	517.1

The class interval containing the \((\frac{N}{2})^{th}\) or 25^th item is 20 – 30. 

Therefore, 20 – 30 is the median class. 

It is known that, 

Median= \(I+\frac{\frac{N}{2}-c}{f}h\)

Here, l = 20, C = 14, f = 14, h = 10, and N = 50 

∴ Median \(=20+\frac{25-14}{14}×10=20+\frac{110}{14}=20+7.85=27.85\)

Thus, mean deviation about the median is given by, 

\(M.D.(M)=\frac{1}{N}\sum_{i=1}^{6}f_i|x_i-M|=\frac{1}{50}×517.1=10.34\)