7. (10 points) A natural number that reads the same from left to right as from right to left is called a "palindrome number", for example: 
909. Then the average of all three-digit palindrome numbers is.
550
【Analysis】A three-digit palindrome is in the form of $A B A$, with a total of 90 such numbers, so the average $=$ the sum of these numbers $\div 90=[101$ $\times(1+2+\cdots+9) \times 10+10 \times(0+1+2+\cdots+9) \times 9] \div 90$, which leads to the conclusion.

【Solution】Solution: A three-digit palindrome is in the form of $A B A$
$A$ has 9 possibilities from 1 to 9, i.e., $1 B 1, 2 B 2, 3 B 3 \cdots$
$B$ has 10 possibilities from 0 to 9, i.e., $A 0 A, A 1 A, A 2 A, A 3 A, \cdots$
There are a total of $9 \times 10=90$ numbers
Therefore, the average $=$ the sum of these numbers $\div 90$
$$
\begin{array}{l}
=[101 \times(1+2+\cdots+9) \times 10+10 \times(0+1+2+\cdots+9) \times 9] \div 90 \\
=(101 \times 45 \times 10+10 \times 45 \times 9) \div 90 \\
=45 \times 10 \times 110 \div 90 \\
=5 \times 110 \\
=550
\end{array}
$$

Therefore, the answer is 550.