Prove or disprove the following inequality.
$$ \frac{\sum_{i = 1}^n a_i}{\sum_{i = 1}^n b_i} \geq \frac{1}{n} \left( \sum_{i = 1}^n \frac{a_i}{b_i} \right), $$
where $a_i \leq b_i$ for all $i = 1, 2, \dots, n$.
I am actually computing the average of some percentages $(a_i / b_i)$ and for some reasons I cannot compute it directly. I can only do the fraction on the left. I am trying to establish this inequality so that I know what I can expect from the computation.