Question

Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams.

Team 1	Team 2	Team 3	Team 4
1	2	0	3
2	3	0	4
0	2	1	4
3	4	1	3
2	4	0	2

What is$S{S}_{\text{between}}$?

Short answer

The value of$S{S}_{\text{between}}=25.75$.

Step-by-step solution

Given Information

Girls from four different soccer teams are to be tested for mean goals scored per game.

Team 1	Team 2	Team 3	Team 4
1	2	0	3
2	3	0	4
0	2	1	4
3	4	1	3
2	4	0	2

Explanation

To find the value of$S{S}_{\text{between}}$:

From our Table, we can calculate

$s_1=8,s_2=15,s_3=2,s_4=16$

We now can calculate:

${\mathbf{SS}}_{\text{between}}=\sum \left[\frac{{\left(s_j\right)}^2}{n_j}\right]-\frac{{\left(\sum s_j\right)}^2}{n}$

$S{S}_{\text{between}}=\frac{s_1^2}{5}+\frac{s_2^2}{5}+\frac{s_3^2}{5}+\frac{s_4^2}{5}-\frac{{\left(s_1+s_2+s_3+s_4\right)}^2}{20}$

$\text{where}{n}_1=n_2=n_3=n_4=5\text{and}n=n_1+n_2+n_3+n_4=20$

We calculate,

$\frac{(8{)}^2}{5}+\frac{(15{)}^2}{5}+\frac{(2{)}^2}{5}+\frac{(16{)}^2}{5}-\frac{(8+15+2+16{)}^2}{20}$

${\mathbf{SS}}_{\text{between}}=109,8-84.05=\mathbf{25}\mathbf{.}\mathbf{75}$