Calculate co-efficient of variation from the following data : Age-group (Less than): 10 20 30 40 50 60 70 80 Population in thousands : 10 26 51 81 107 120 125 130
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Answer:
For Batsman A
S. No. Score
(XA) Deviation from mean
(xA=XA-XA) x
2
A
1
2
3
4
5
6
7
8
9
10 12
115
6
73
7
19
119
36
84
29 −38
65
−44
23
−43
−31
69
−14
34
−21 144
4225
1936
529
1849
961
4761
196
1156
441
N = 10 ΣxA = 500 Σx
2
A
=17498
X=
ΣX
N
=
500
10
=50SD (σA)=
√
Σx
2
A
N
=
√
17498
10
=41.83Coefficient of Variation=
σA
XA
×100=
41.83
50
×100=83.66%
For Batsman B
S. No. Score
XB Deviation from Mean
(xB=XB-XB) x
2
B
1
2
3
4
5
6
7
8
9
10 47
12
76
42
4
51
37
48
13
0 14
−21
43
9
−29
18
4
15
−20
−33 196
441
1849
81
841
324
16
225
400
1089
N = 10 ΣxB = 330 Σx
2
B
=5462
XB=
ΣX
N
=
330
10
=33SD (σB)=
√
Σx
2
B
N
=
√
5462
10
=
√
546.2
=23.37Coefficient of Variation=
σB
XB
×100=
23.37
33
×100=70.82%
Since average score of A is more than B, he is better as run-getter but since, coefficient of variance is less for B, therefore B is more consistent.
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