# Compute coefficient of variation for team A and team B. (Given:26=5.099,22=4.6904) No. of goals 0 1 2 3 4 No. of matches played by team A 18 7 5 16 14 No. of matches played by team B 14 16 5 - Mathematics and Statistics

Sum

Compute coefficient of variation for team A and team B. ("Given": sqrt(26) = 5.099, sqrt(22) = 4.6904)

 No. of goals 0 1 2 3 4 No. of matches played by team A 18 7 5 16 14 No. of matches played by team B 14 16 5 18 17

Which team is more consistent?

#### Solution

For team A

Let f1 denote no. of goals of team A.

 No. of goals (xi) No. of matches (f1i) f1ixi f1ixi2 0 18 0 0 1 7 7 7 2 5 10 20 3 16 48 144 4 14 56 224 N1 = 60 ∑f1ixi = 121 ∑f1ixi2 = 395

bar("x"_1) = (sum"f"_"1i""x"_"i")/"N"_1

= (121)/(60)
= 2.0167
Standard deviation,

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

= 395/60 - (2.0167)^2

= 6.5833 − 4.0671
= 2.5162
∴ sigma_"x1"=sqrt2.5162 = 1.5863
Co-efficient of variance;

C.V (x1) = sigma_"x1"/bar("x"_1) xx 100

= (1.5863)/(2.0167) xx 100
= 78.66%

For team B

Let f2 denote no. of goals of team B.

 No. of goals (xi) No. of matches (f2i) f2ixi f2ixi2 0 14 0 0 1 16 16 16 2 5 10 20 3 18 544 162 4 17 68 272 N2 = 70 ∑f2ixi = 148 ∑f2ixi2 = 470

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

= (148)/(70)
= 2.1143
Standard deviation,

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

= 470/70- (2.1143)^2

= (6.7143 − 4.46703)
= 2.244
∴ sigma_"x2"= sqrt2.244 = 1.4980
Co-efficient of variance;

C.V. (x2) = sigma_"x2"/bar("x"_2) xx 100

= 1.4980/2.1143xx100
= 70.85%

Since, C.V. of team A > C.V. of team B.
∴ team B is more consistent.

Concept: Coefficient of Variation
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