Will Rogers phenomenon

The Will Rogers phenomenon is the apparent paradox obtained when moving an element from one set to another set raises the average values of both sets.

Numerical example

Consider the sets R and S

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:R={1, 2, 3, 4}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:S={5, 6, 7, 8, 9}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The arithmetic mean of R is 2.5, and the arithmetic mean of S is 7.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

However, if we move 5 from S to R, producing

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:R={1, 2, 3, 4, 5}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:S={6, 7, 8, 9}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

then the arithmetic mean of R increases to 3, and the arithmetic mean of S increases to 7.5

~ ~ ~ ~ ~ ~ ~ ~ ~ ~