To find the median, first arrange the data in ascending order:
\[
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
\]
Since there are 10 data points (an even number), the median is the average of the 5th and 6th values:
\[
\text{Median} = \frac{26 + 29}{2} = \frac{55}{2} = 27.5
\]
Thus, the correct answer is \( 27.5 \).