Continuous Mean Deviation
For calculating the mean deviation in continuous series the process remains the same. The only difference is that here we have to obtain the mid-point of the various classes and take deviation of these points from the median. The formula is just same as:
M.D. Σ f |D| / N
Illustration:
Find the median and mean deviation of the following data
|
Size
|
frequency
|
size
|
frequency
|
|
0-10
|
7
|
40-50
|
16
|
|
10-20
|
12
|
50-60
|
14
|
|
20-30
|
18
|
60-70
|
8
|
|
30-40
|
25
|
|
|
Solution:
Computation of median and mean deviation
|
Size
|
F
|
c.f
|
m.p .m
|
|m - 35.2 | |D|
|
F |D|
|
|
0-10
|
7
|
7
|
5
|
30.2
|
211.4
|
|
10-20
|
12
|
19
|
15
|
20.2
|
242.4
|
|
20-30
|
18
|
37
|
25
|
10.2
|
183.6
|
|
30-40
|
25
|
62
|
35
|
0.2
|
5.0
|
|
40-50
|
16
|
78
|
45
|
9.8
|
156.8
|
|
50-60
|
14
|
92
|
55
|
19.8
|
277.2
|
|
60-70
|
8
|
100
|
65
|
29.8
|
238.4
|
|
|
N =100
|
|
|
Σ f |D| =
|
1314.8
|
Med. Size of N/2 th item = 100/2 = 50th item
Median lies in the class 30-40
Med. = L + n/2 - c.f / f xi
L = 30, N / 2 = 50, c.f = 37, f = 25, I = 10
Med. = 30+ 50 - 37 / 25 x 10 = 30 + 5.2 = 35.2
Md = Σ f |D| / N = 1314.8 / 10 = 13.148
Calculate the mean deviation and its coefficient from the following data
|
Class
|
frequency
|
Class
|
frequency
|
|
0-10
|
5
|
40-50
|
20
|
|
10-20
|
8
|
50-60
|
14
|
|
20-30
|
12
|
60-70
|
12
|
|
30-40
|
15
|
70-80
|
6
|
Solution:
Since noting is special we will calculate mean deviation from median
Calculation of mean deviation
|
Class
|
Frequency
|
c.f
|
m.p.m
|
|m - 43 | |D|
|
F |D|
|
|
0-10
|
5
|
5
|
5
|
38
|
190
|
|
10-20
|
8
|
13
|
15
|
28
|
224
|
|
20-30
|
12
|
25
|
25
|
18
|
216
|
|
30-40
|
15
|
40
|
35
|
8
|
120
|
|
40-50
|
20
|
60
|
45
|
2
|
40
|
|
50-60
|
14
|
74
|
55
|
12
|
168
|
|
60-70
|
12
|
86
|
65
|
22
|
264
|
|
70-80
|
6
|
92
|
75
|
32
|
192
|
|
|
N = 92
|
|
|
Σ f |D| =
|
1414
|
Med = size of N/2 th item = 92/2 = 46th item
Median lies in the class 40-50
Med = L+ N/2 -cf. / f xi
L = 40 N/2 = 46 c.f = 40 f = 20 I = 10
∴ Median = 40 + 46 - 40 / 20 x 10 = 40 + 3 = 43
M.D = Σ f |D| / N = 1414 / 92 = 15.37
Coefficient of M.D = M.D / median = 15.37 / 43 = 0357.