Let's say that there are two sets with number of elements n1 and n2 and averages X1 and X2. The sum of the values of both the sets will be n1X1+n2X2 and the number of elements combined will be n1+n2. Since X1<X2, we can say that: (n1+n2)X1<n1X1+n2X2<(n1+n2)X2
⇒
(n1+n2)X1
n1+n2
<
n1X1+n2X2
n1+n2
<
(n1+n2)X2
n1+n2
X1<X<X2 ∴ The combined average of two sets always lies between the individual averages, i.e. X1<X<X2