Question

The following is the record of goals scored by team A in a football session:

No. of goals scored	0	1	2	3	4
No. of matches	1	9	7	5	3

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Answer 1

The mean and the standard deviation of goals scored by team A are calculated as follows

No. of goals scored	No. of matches	$fx_i$	$x_1^2$	$fx_1^2$
0	1	0	0	0
1	9	9	1	9
2	7	14	4	28
3	5	15	9	45
4	3	12	16	48
-	25	50	-	130

$Mean=\frac{\sum_{i=1}^{5}f_ix_i}{\sum_{i=1}^{5}f_i}=\frac{50}{25}=2$

Thus, the mean of both the teams is same.

$σ=\frac{1}{N}√N\sum{f_i}{x_i}^2-(\sum_{f_i}{x_i})^2$

$=\frac{1}{25}√25 ×130-(50)^2$

$\frac{1}{25}√750$

$=\frac{1}{25}×27.38$

=1.09

The standard deviation of team B is 1.25 goals.

The average number of goals scored by both the teams is same i.e., 2. Therefore, the team with lower standard deviation will be more consistent.

Thus, team A is more consistent than team B.