Bugs –
The Case-Shiller index uses repeat sales to overcome some of the problems with median prices, primarily the biases due to change in mix of sales.

Since any particular house is typically only sold every few years there are some sampling issues, and they make use of estimation theory.

It’s laid out in the following …
http://macromarkets.com/csi_housing/documents/tech_discussion.pdf

All those engineers out there might appreciate it, but others might want to take a class in Random Signal Theory before reading the details.