If the sum of a set of numbers is bigger, will the average of the set of numbers be bigger too?

Question

If the sum of a set of real numbers $X$ is bigger than the sum of a set of numbers $Y$, will the average of $X$ be bigger than $Y$ and vice versa?

What is a proof either way?

Answer 1

You are in fact asking if

$$a>b\implies \frac ac>\frac bd$$ for some numbers $a,b,c,d$ (in your case $c,d$ are integers, but that does not change much).

This clearly does not hold, unless $c=d$.

Answer 2

$2+6>7$ but $(2+6)/2<7/1=7.$