What makes you believe that housing is not included? Consider using a search engine (Google is pretty good) and using keywords like "cpi shelter weight" or "cpi housing weight". The BLS has a page on the subject.
Sorry, I read the 2nd sentence as removing housing entirely, for some reason. I see that's not what they're saying, they're just talking about the relative weight of the thing.
My apologies for not knowing offhand everything that goes into the CPI, and not googling it for more context, I was just asking questions on the internet instead. I should've known better than to hope for learning something from my fellow humans.
