Mean of 4-digit even numbers 'aabb'

Any 4-digit number of the form 'aabb' can be represented as: $1000a + 100a + 10b + b = 1100a + 11b$

For the number to be an even natural number:

• $a \in \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ ($a > 0$)
• $b \in \{0, 2, 4, 6, 8\}$ (must be even)

Since the choices of $a$ and $b$ are independent:

• Average of $a = \frac{1 + 9}{2} = 5$
• Average of $b = \frac{0 + 8}{2} = 4$

Therefore, the mean of all such numbers is: $1100(\text{mean of } a) + 11(\text{mean of } b) = 1100(5) + 11(4) = 5500 + 44 = 5544$