Mobile phone usage provides a wealth of information, which can be used to better understand the demographic structure of a population. In this paper we focus on the population of Mexican mobile phone users. Our first contribution is an observational study of mobile phone usage according to gender and age groups. We were able to detect significant differences in phone usage among different subgroups of the population. Our second contribution is to provide a novel methodology to predict demographic features (namely age and gender) of unlabeled users by leveraging individual calling patterns, as well as the structure of the communication graph. We provide details of the methodology and show experimental results on a real world dataset that involves millions of users.