In two old statistics textbooks, I found the following pictures:- Without any explanation, they both inferred the following:-
When it is right skewed (as in fig. 3.2), mean > median. (And is the otherwise for the left skewed.)
- I wonder if the claim is always true?
- If it is, is there any simple proof? [By simple, I mean something like by inspection or simple logical reasoning but not deep into the statistical theory please.]