Find the mean deviation about median for the following data:
|
Marks |
Number of girls |
|
0-10 |
6 |
|
10-20 |
8 |
|
20-30 |
14 |
|
30-40 |
16 |
|
40-50 |
4 |
|
50-60 |
2 |
The following table is formed.
-
Marks
Number of girls fi
Cumulative frequency (c.f.)
Mid-point xi
|xi – Med.|
fi |xi – 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
or 25th item is 20 – 30.
Therefore, 20 – 30 is the median class.
It is known that,
Here, l = 20, C = 14, f = 14, h = 10, and N = 50
∴ Median =
Thus, mean deviation about the median is given by,
