1. **State the problem:** We need to find the median number of miles Jenna cycled over a 7-week period with the data: 36, 42, 28, 52, 48, 36, 31. 2. **Recall the formula and rule for median:** The median is the middle value in an ordered data set. For an odd number of data points $n$, the median is the value at position $\frac{n+1}{2}$ when the data is sorted. 3. **Order the data from least to greatest:** $$28, 31, 36, 36, 42, 48, 52$$ 4. **Find the position of the median:** Since $n=7$, the median position is: $$\frac{7+1}{2} = \frac{8}{2} = 4$$ 5. **Identify the median value:** The 4th value in the ordered list is $36$. 6. **Conclusion:** The median number of miles Jenna cycled is **36** miles.