Assume we have $N$ non-negative numbers $X_1,..., X_N$ with the arithmetic mean $\bar{X}$.
What is the expected value of the portion of their sum that the summands larger than $\bar{X}$ account for?
Example: $1, 3, 4, 6, 8$. Only $6$ and $8$ are larger than the mean. $6+8=14$, which is $\approx64\%$ of the total sum $22$.
This has very practical applications, e.g. "What portion of our sales do the items that sell better than average account for?"
In general, the aforementioned portion can be anywhere between $0$ and $1$. E.g. for $0, 0, 0, 1$, the portion is $100\%$. For $1, 1, 1, 2$, the portion is $40\%$ and tends to $0\%$ as we add more numbers $1$.
And yet there seem to be patterns. For instance, in my numerical experiments with uniformly distributed random variables, the portion seems to be around $75\%$.