I read in a publication that the average salary for lawyers in America is $\bar x=\$163,595$. Of these salaries, the average for men is $\bar x_m=\$183,687$, and for women, it is $\bar x_w=\$163,595$. I'm thinking, how is it possible for the average of women's salary be equal the average of the entire set?
Note that $\bar x_w = \bar x < \bar x_m$, and $\bar x_w,\, \bar x,\, \bar x_m > 0$.
Can we prove that this is possible/impossible? Can we find 1 simple example where $\bar x_w = \bar x$ (given $\bar x_w,\, \bar x,\, \bar x_m > 0$, and $\bar x_m > \bar x$) is possible?