Skewed poll results?

Question

I have an asignment:

Students on various universities were given polls where they rated their school on a scale:

1. Very bad
2. Far below average
3. Below average
4. Average
5. Above average
6. Far above average
7. Excellent

After evaluating the individual averages for each university, they computed an average of those and the result was $4.94$.

This means that most of the universities are above average.

What dou you think of that?

My first thought is that there's a problem with the way the data is presented.

Instead of taking the average of all the answers, they first computed an average of each university individually and then they computed average of these averages.

Is it a problem though?

Let $s_k$ be the number of students at the $k$-th university and $u$ the number of universities. When I take a regular average, I get: $$ S = \sum_{i = 1}^{u} s_k $$

$$\overline{x} = \frac{1}{S} \sum_{i = 1}^{S} x_i $$

but when I take the average of averages: $$\overline{y} = \frac{1}{u} \left( \sum_{k = 1}^{u}\frac{1}{s_k} \sum_{i = 1}^{s_k} y_i \right).$$

But $\overline{x} \neq \overline{y}$.

Would it be a fair evaluation if they took weighted average instead? Would $s_k$ be a fair weight?