Arithmetic Mean of Permutations

The digits are 1, 4, 2, 1. The sum of digits is $1 + 4 + 2 + 1 = 8$. Since each digit occupies each position with equal symmetry in all permutations, the average value of each digit position (thousands, hundreds, tens, units) is the average of the digits: $\text{Average digit value} = \frac{1 + 4 + 2 + 1}{4} = 2$

Since the average digit at every place is 2, the arithmetic mean of all permutations is: $2222$