**Question:**

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

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?

**Solution:**

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

Mean $=\frac{\sum_{i=1}^{5} f_{i} x_{i}}{\sum_{i=1}^{5} f_{i}}=\frac{50}{25}=2$

Thus, the mean of both the teams is same.

$\sigma=\frac{1}{N} \sqrt{N \sum f_{i} x_{i}{ }^{2}-\left(\sum f_{i} x_{i}\right)^{2}}$

$=\frac{1}{25} \sqrt{25 \times 130-(50)^{2}}$

$=\frac{1}{25} \sqrt{750}$

$=\frac{1}{25} \times 27.38$

$=1.09$

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.