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	16	5	18	15

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)	No. of matches (f1i)	No. of matches (f2i)	f1ixi	f2ixi	f1ixi2	f2ixi2
0	19	16	0	0	0	0
1	6	16	6	16	6	16
2	5	5	10	10	20	20
3	16	18	48	54	144	162
4	14	15	56	60	224	240
	N1 = 60	N2 = 70	f1ixi = 120	f2ixi = 140	f1ixi2 = 394	f2ixi2 = 438

For Team A,

`bar("x"_1) = (sum"f"_"1i""x"_"i")/"N"_1 = (120)/(60) = 2`
Standard deviation,

`sigma_("x"_1)^2 = 1/"N"_1sum"f"_"1i""x"_"i"^2- (bar"x"_1)^2 `

`sigma_("x"_1)^2 = 394/60 - (2)^2`

`sigma_("x"_1)^2` = 6.57 − 4

`sigma_("x"_1)^2` = 2.57

∴ `sigma_"x1" = sqrt2.57 = 1.60`

Co-efficient of variance;

C.V (x₁) = `sigma_"x1"/bar("x"_1) × 100 = (1.60)/(2) × 100 = 80%`

For Team B,

`bar("x"_2) = (sum"f"_"2i""x"_"i")/"N"_2 = (140)/(70) = 2`

Standard deviation,

`sigma_("x"_2)^2 = 1/"N"_2sum"f"_"2i""x"_"i"^2- (bar"x"_2)^2 `

`sigma_("x"_2)^2 = 438/70- (2)^2`

`sigma_("x"_2)^2` = 6.26 − 4

`sigma_("x"_2)^2` = 2.26

∴ `sigma_"x2"= sqrt(2.26)` = 1.50

Co-efficient of variance;

C.V. (x₂) = `sigma_"x2"/bar("x"_2) × 100 = 1.50/2 × 100 = 75%`

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

∴ Team B is more consistent.