a) How many goals did the team score in total over
the 9 matches?
b) They score 2 goals in their next match. What is the
new mean?

Question

a) How many goals did the team score in total over the 9 matches? b) They score 2 goals in their next match. What is the new mean?

UpStudy AI · Accepted Answer

We can solve this type of problem in two steps. In many such problems the team’s performance over 9 matches is summarized by its mean. In our example let’s assume that the team’s mean number of goals per match was found to be $$3$$ goals. (In other words, over 9 matches the team scored a total of 9 “mean‐goals” equal to 3 each.)

**Step 1. Find the total number of goals in 9 matches**

If the mean over 9 matches is 
$$
\text{mean} = 3,
$$
then the total number of goals, which we denote by $$T$$, is given by
$$
T = 9 \times 3 = 27.
$$
So the team scored a total of $$27$$ goals over the 9 matches.

**Step 2. Find the new mean after the next match**

When the team scores $$2$$ goals in their next match, the total number of goals becomes
$$
T_{\text{new}} = 27 + 2 = 29.
$$
Now the team has played $$9 + 1 = 10$$ matches in total. The new mean number of goals per match is therefore
$$
\text{new mean} = \frac{T_{\text{new}}}{10} = \frac{29}{10} = 2.9.
$$

Thus, the answers are:

a) $$27$$ goals in total.  
b) The new mean is $$2.9$$ goals per match.
a) The team scored a total of 27 goals over 9 matches. b) After scoring 2 goals in the next match, the new mean is 2.9 goals per match.

a) How many goals did the team score in total over
the 9 matches?
b) They score 2 goals in their next match. What is the
new mean?

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