Methods, apparatus, systems, and articles of manufacture to perform computer-based monitoring of audiences of network-based media using information theory to estimate intermediate level unions are disclosed. An example apparatus to determine a deduplicated, census-based audience metric of media includes panel union calculator circuitry to calculate a threshold statistic corresponding to an intermediate union of a panel hierarchy, and census union calculator circuitry to calculate a deduplicated audience value corresponding to the intermediate union of the census hierarchy based on the threshold statistic.

A system and method of using printed mail to retrieve consumer interest data includes printing a scannable code on a printed mail piece, sending the printed mail piece out for postal delivery to a consumer and receiving a request from a mobile device to access a server-based resource based on the consumer scanning the scannable code on the printed mail piece. The system and method includes providing access to the server-based resource, the server-based resource serving questions regarding consumer interests to the mobile device, and retrieving consumer interest data based on the responses of the consumer to the questions.