We need to put the data in size order first:
9.2, 9.9, 10.9, 12.3, 12.4, 15.4, 27.7, 34.8, 35.4, 38.6.
The median is the central value within the dataset.
There are ten data values, an even number, so we need to average the central pair:
(12.4+15.4)/2=13.9, the median.