Google Pagerank (PR) Vs. Alexa traffic rank

Google Pagerank and Alexa Traffic Rank though both attempted to rank the websites.

Alexa Traffic Rank - This is a ranking system set by alexa.com (a subsidiary of amazon.com)

Google rank web pages according to its popularity and importance based on inbound links and Alexa rank the websites according to its traffic, which is randomly sampled. That is the main reason of showing a different and contradicting statistics, specially, for a relatively small and new websites.

Alexa Rank is more important than page rank and basic thing is to improve Alexa Rank so that people trust you.