Here's a mathematical proof that demonstrates why this can't happen:
Suppose that we have the data set :
A1, A2,.....An where An is the largest value
And suppose that B is a mean that is greater than An......and suppose that we assume that
[ A1 + A2 +.....+An] / n = B is true ........ multiply both sides by n
A1 + A2 +.....+ An = Bn .... implies that
A1 + A2 +.......+ An = B + B + B........ summmed "n" times
But B > than any term on the left.....and since we have the same number of terms on each side, the right side must be larger than the left side.....thus, they cannot be equal....and our assumption is false......so, the mean cannot be greater than any individual value in a set of data
