Question

Compute coefficient of variation for team A and team B:

No. of goals	0	1	2	3	4
No. of matches played by team A	19	6	5	16	14
No. of matches played by team B	16	14	10	14	16

Which team is more consistent?

Answer 1

Let f₁ denote no. of goals of team A and f₂ denote no. of goals of team B.

No. of goals (xi)	f1i	f1ixi	f1ix12
0	19	0	0
1	6	6	6
2	5	10	20
3	16	48	144
4	14	56	224
	N1 = 60	`sumf_(1"i")x__"i"` = 120	`sumf_(1"i")x_1^2` = 394

`bar(x)_1 = (sumf_(1"i")x_"i")/"N"_1 = 120/60` = 2

`sigma_(x_1)^2 = 1/"N"_1 sumf_(1"i")x_"i"^2 - (barx_1)^2 = 394/60 - 2^2` = 6.5666 – 4 = 2.5666

∴ `sigma_(x_1) = sqrt(2.5666)` = 1.60

C.V. of team A = `100 xx sigma_(x_1)/bar(x)_1`

= `100 xx 1.60/2`

= 80%

No. of goals (xi)	f2i	f2ixi	f2ix12
0	16	0	0
1	14	14	14
2	10	20	40
3	14	42	126
4	16	64	256
	N2 = 70	`sumf_(2"i")x__"i"` = 140	`sumf_(2"i")x_1^2` = 436

`bar(x)_2 = (sumf_(2"i")x_"i")/"N"_2 = 140/70` = 2

`sigma_(x_2)^2 = 1/"N"_2 sumf_(2"i")x_"i"^2 - (barx_2)^2= 436/70 - 2^2` = 6.2285 – 4 = 2.2285

∴ `sigma_(x_2) = sqrt(2.2285)` = 1.49

C.V. of team B = `100 xx sigma_(x_2)/bar(x)_2`

= `100 xx 1.49/2`

= 74.5%

Since C.V. of team A > C.V. of team B,

Team B is more consistent.