As a high school student I am not sure why this following formula which is used as a relation between mean, median and mode found to hold for unimodal distribution, is called empirical:$$ mean-mode=3(mean-median)$$ is there really no mathematical proof? My text book says that this is completely based on symmetry. Can some one help me to clarify this? Is there any existing proof in higher classes? Thanks in advance.
EDIT:Later I found this in cross validated but that's not quite accessible to me I will be happy if I get a simpler version or at least an intuitive understanding.