Step 1: Arrange the numbers in ascending order: 
\[
17, 18, 24, 25, 35, 36, 46
\]
Step 2: Find the middle number (median) in the sorted list. 
Since there are 7 numbers (odd count), median is the \(\frac{7+1}{2} = 4^\text{th}\) number. 
Step 3: Identify the 4th number: 
The 4th number in the list is 25. 
Hence, the median is \(\boxed{25}\).