I have two sets of numbers as follows: $$X = \{x_1, x_2, ..., x_n\}\\ Y = \{y_1, y_2, ..., y_n\}$$ And a number $r$.
Let $x^\ast$ and $y^\ast$ is average values of set $X$ and $Y$ respectively.
With the following conditions: $|r-x_1|+|r-x_2|+...+|r-x_n|\geqslant|r-y_1|+|r-y_2|+...+|r-y_n|$ and $|x^\ast-x_1|+|x^\ast-x_2|+...+|x^\ast-x_n|=|y^\ast-y_1|+|y^\ast-y_2|+...+|y^\ast-y_n|$
Whether the following statement is true: $$|r-x^\ast| \geqslant |r-y^\ast|$$