Step 1: List the natural numbers from 1 to 9.
The natural numbers from 1 to 9 are:
\[
1, 2, 3, 4, 5, 6, 7, 8, 9
\]
Step 2: Calculate the sum of these numbers.
The sum of the numbers from 1 to 9 is:
\[
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
\]
Step 3: Calculate the number of terms.
There are 9 terms in the set.
Step 4: Apply the formula for arithmetic mean.
The formula for the arithmetic mean is:
\[
\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Number of terms}} = \frac{45}{9} = 5
\]
Step 5: Conclusion.
Thus, the arithmetic mean of the natural numbers from 1 to 9 is 5. Therefore, the correct answer is (A).