for example, that average wages have risen faster than CPI inflation does not imply a claim "wages have risen faster than inflation" is also true.

the latter claim may be require further definition in order to evaluate at all. (do we mean median wages? your wages or mine? what measure or concept of inflation?)

but if you are supercilliating the claim is true and that your interlocutor is naive or mistaken, well, we are all usually guilty of the sins we accuse of others. /fin