I am teaching a year 8 class data, and they came across this question which they didn't know how to do.
The question is: Annie averages 15 points per game for the first 3 games of the AFL season. Over the next two weeks she scores 18 and 22 points. Find her average score over the 5 games?
This is my working
Find the average of the next 2 games $$\frac {(18+22)}{2} = 20$$
I then find the average of the 2 averages $$\frac {(15+20)}{2}= 17.5$$
Because you can't have an average of 17.5 points, would you round up or down?
As mentioned in the comments, taking an average of an average won't provide an accurate picture of the average score over five games.
Let's say Annie scores exactly $15$ points in each of her first three games (providing an average of $15$). Her average score over the five games would be
$$\frac{15+15+15+18+22}{5}=17$$
though it doesn't matter what combination you use to get an average of $15$; you will always have a five-game average of $17$ (i.e. having $14$ points, then $15$, then $16$ would still give you an average score over five games of $17$).