Question

9. Compute coefficient of variation for team A
and team B. (Given : 126 = 5.099,
22 = 4.6904)
No. of goals
01234
No. of matches 18 7 5 | 16 | 14
played by team A
No. of matches | 14 | 16 | 5 18 17
played by team B
Which team is more consistent?​

Answer 1

Answer:

For calculating the coefficient of variation for team A and team B, let us first calculate certain information referring to the calculated data from the figure of the tables attached below:  

Step 1:

For Team A:

Mean,  ¯X = ∑fiXi / ∑fi = 121 / 60 = 2.016

Standard deviation, σ = √ [{(∑fiXi^2)/∑fi} – {∑fiXi/∑fi }²]

⇒ σ = √ [(395/60) – (2.016)²]

⇒ σ = √ [2.52]

⇒ σ = 1.587

Coefficient of variation, C.O.V. = [σ/¯X] * 100 = (1.587/2.016) * 100 = 78.72

Step 2:

For Team B:

Mean,  ¯X = ∑fiXi / ∑fi = 148 / 70 = 2.114

Standard deviation, σ = √ [{(∑fiXi^2)/∑fi} – {∑fiXi/∑fi}²]

⇒ σ = √ [(470/70) – (2.114)²]

⇒ σ = √ [2.246]

⇒ σ = 1.498

Coefficient of variation, C.O.V. = [σ/¯X] * 100 = (1.498/2.114) * 100 = 70.86

Step 3:

The lesser the value of the coefficient of variation, the lesser the dispersion around it's mean and more precise will be the estimate i.e., the more consistent will be the team.

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

∴ Team B is more consistent.