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

$x_i$	$f_i$	$f_i{x}_i$	$x_i^2$	$f_i{x}_i^2$
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
Total	25	50		130

$Mean=\frac{{\sum }_{i=1}^5{f}_i{x}_i}{{\sum }_{i=1}^5{f}_i}=\frac{50}{25}=2$

Given mean of team $B=2$
Mean of both the teams is same.

Now,$\sigma =\frac{1}{N}\sqrt{N\sum f_i{X}_i^2-{(\sum f_i{X}_i)}^2}$
$=\frac{1}{25}\sqrt{25\times 130-(50{)}^2}$
$=\frac{1}{25}\sqrt{750}$
$=\frac{1}{25}\times 27.38$
$=1.09$
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 $B$.