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 25th 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,

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