b) They score 2 goals in their next match. What is the new mean?

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Suppose that before the next match the team had played $$ n $$ matches and had a mean score of $$ \mu $$ goals per match. Then the total number of goals scored so far is

$$
T = n \mu.
$$

If in their next match they score 2 goals, the new total becomes

$$
T_{\text{new}} = n\mu + 2.
$$

Also, the total number of matches becomes

$$
n_{\text{new}} = n + 1.
$$

Thus, the new mean is given by

$$
\mu_{\text{new}} = \frac{n\mu + 2}{n+1}.
$$

This is the new mean in terms of the original number of matches $$ n $$ and the original mean $$ \mu $$.
The new mean is calculated by adding 2 to the total goals and dividing by the new number of matches, so $$ \mu_{\text{new}} = \frac{n\mu + 2}{n+1} $$.

b) They score 2 goals in their next match. What is the
new mean?

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