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Unformatted text preview: mean and median from the
following series.
Age in years
No.of
persons
010
20
1020
25
2030
32
3040
40
4050
42
5060
35
6070
10
7080
8
Also compute coefficient of mean deviation.
Solution: X m f 010
1020
2030
3040
4050
5060
6070
7080 5
15
25
35
45
55
65
75 m−A
c
(A=35,C=10) 20
25
32
40
42
35
10
8
212 x = A+ ∑ fd × c N
32
= 35 +
× 10
212 = 35 + d= 3
2
1
0
1
2
3
4 D=
fd 60
50
32
0
42
70
30
32
32 m−x fD 31.5
21.5
11.5
1.5
8.5
18.5
28.5
38.5 630.0
537.5
368.0
60.0
357.0
647.5
285.0
308.0
3193.0 320
= 35 + 1.5 = 36.5
212
154 ∑f D 3193
= 15.06
N
212
Calculation of median and M.D. from median
M.D. = = X m f c.f D = mMd f D 010
1020
2030
3040
4050
5060
6070
7080 5
15
25
35
45
55
65
75 20
25
32
40
42
35
10
8 20
45
77
117
159
194
204
212 32.25
22.25
12.25
2.25
7.75
17.75
27.75
37.75
Total 645.00
556.25
392.00
90.00
325.50
621.25
277.50
302.00
3209.50 N
212
=
= 106
2
2
l = 30, m = 77, f = 40, c = 10
N
−m
2
Median = l +
×c
f
106  77
= 30 +
× 10
40
29
= 30 +
4
= 30 + 7.25 = 37.25
∑f  D 
M. D. =
N
3209.5
=
= 15.14
212
M.D
Coefficient of M.D =
Median
15.14
= 0.41
=
37.25
155 7.5.6 Merits and Demerits of M.D :
Merits:
1. It is simple to understand and easy to compute.
2. It is rigidly defined.
3. It is based on all items of the series.
4. It is not much affected by the fluctuations of sampling.
5. It is less affected by the extreme items.
6. It is flexible, because it can be calculated from any
average.
7. It is better measure of comparison.
Demerits:
1. It is not a very accurate measure of dispersion.
2. It is not suitable for further mathematical calculation.
3. It is rarely used. It is not as popular as standard deviation.
4. Algebraic positive and negative signs are ignored. It is
mathematically unsound and illogical.
7.6 Standard Deviation and Coefficient of variation:
7.6.1 Standard Deviation :
Karl Pearson introduced the concept of standard deviation
in 1893. It is the most important measure of dispersion and is
widely used in many statistical...
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 Winter '08
 Moshiri
 Business

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