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

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(A) First,we calculate the mean and standard deviation for team $A$.
$x_i$ $f_i$ $f_i x_i$ $f_i x_i^2$
$0$ $1$ $0$ $0$
$1$ $9$ $9$ $9$
$2$ $7$ $14$ $28$
$3$ $5$ $15$ $45$
$4$ $3$ $12$ $48$
Total $25$ $50$ $130$

Mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i} = \frac{50}{25} = 2$.
Standard deviation $\sigma = \sqrt{\frac{\sum f_i x_i^2}{N} - (\bar{x})^2} = \sqrt{\frac{130}{25} - (2)^2} = \sqrt{5.2 - 4} = \sqrt{1.2} \approx 1.095$.
For team $B$,mean $= 2$ and $\sigma = 1.25$.
Since the mean is the same for both teams,the team with the lower standard deviation is more consistent. Since $1.095 < 1.25$,team $A$ is more consistent.

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