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Question

Goals scored by two teams A and B in football matches were as follows:
No. of Goals in a match : 0 1 2 3 4
No.of Matches: A : 27 9 8 5 4
B : 17 9 6 5 3
Find the team which is more consistent in its performance.

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Solution

For Team A
X f fX Deviation from mean
xA=X-XA
xA2 fxA2
0
1
2
3
4
27
9
8
5
4
0
9
16
15
16
−1.06
−0.06
0.94
1.94
2.94
1.12
0.0036
0.88
3.76
8.64
30.24
0.03
7.04
18.8
34.56
Σf = 53 ΣfX = 56 ΣfxA2=90.68

XA=ΣfXΣf=5653=1.06SDA=ΣfxA2Σf=90.6853=1.71 =1.31Coefficient of variation=SDAXA×100=1.311.06×100=123.6%
For Team B
X f fX Deviation from mean
xB=X-XB
xB2 fxB2
0
1
2
3
4
17
9
6
5
3
0
9
12
15
12
−1.2
−0.2
0.8
1.8
2.8
1.44
0.04
0.64
3.24
7.84
24.48
0.36
3.84
16.2
23.52
Σf = 40 ΣfX= 48 ΣfxB2=68.4

XB=ΣfXΣf=4840=1.2SDB=ΣfxB2Σf=68.440=1.71=1.31Coefficient of variation=SDBXB×100 =1.311.2×100=109.1%
Since, coefficient of variation is lesser for team B, it is more consistent.

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